Problems on profitable product mix

1. Present the following information to show to the management

 The marginal product cost and the contribution per unit
 The total contribution and profits resulting from each of the following
mixtures
 The proposed sales mix to earn a profit of RS.250 and Rs.300 with total
sales of A and B being 300 units
Product A Product B
RS. Rs.
Direct materials (per unit) 10 9
Direct wages (per unit) 3 2
Sales price (per unit) 20 15
Fixed expenses RS.800
Variable expenses are allocated to
products of 100% of direct wages

Sales mixtures
 100 units of product A and 200 units of product B
 150 units of product A and 150 units of product B
 200 units of product A and 100 units of product B

2. Ambika condiments bring out two products Suchi and Ruchi, which is popular in
market. The management has the option to alter the sales mix of the two products
from out of the following combinations
Option Suchi (units) Ruchi (units)
I 800 600
II 1600 -
III - 1300
IV 1100 500

The per; unit production cost and sales data are

Particulars Suchi Ruchi
Direct materials (Rs.) 25 30
Direct labour (hours) 10 12
Selling price Rs. 75 90

Variable factory overhead is 100% of direct labour cost for both products.
Common fixed overhead for both products Rs.10, 000
You are required to
 Prepare a marginal cost statement for the two products
 Evaluate the options and identify the most profitable sales mix
Direct labour hour rate Rs.2/-

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 3. ABC ltd manufactures 3 products A, B and C from common facilities. The
production was standardzed for some months at a mix of 27000 units of product A
and 18000 units of product B and C each
The total fixed costs came to Rs.3, 15,000 per month. At the above production
volumes per month, the variable costs are of the order of RS.9, 00,000 per month.
The cost ratios as among the products (excluding fixed costs) are 2:3:4
respectively for A, Band C. The respective selling process is RS.12, RS 15, and
RS.30 per unit. The company presently suffers a loss. Three proposals for
changed product mix have been suggested. They are:
Product A Product B Product C
Mix one 32000 22000 13000
Mix two 27000 10000 23000
Mix three 25000 5000 30000

Which do you consider the most desirable mix/

4. A company manufactures and markets three products X, Y and Z. All the three
products are made from the same set of machines. Production is limited by
machine capacity. From the data given below, indicate priorities for X, Y and Z
with a view to maximising profits
Product X Product Y Product Z
Raw material cost per unit 11.25 16.25 21.25
Direct labour cost per unit 2.50 2.50 2.50
Other variable cost per unit 1.50 2.25 3.55
Selling price per unit 25.00 30.00 35.00
Standard machine time 39 20.00 28
required per unit in minutes

5. On the basis of the following information in respect of an engineering company,

what is the product mix which gives the highest profit attainable
Particulars (per unit) A B C
Raw materials (in kgs) 10 6 15
Labour hours at RS.1 per hour 15 25 20
Selling price 125 100 200
Maximum production (units) 6000 4000 3000
100000 kgs of raw materials are available at 10 per kg

6. The following particulars are obtained from the records of a manufacturing

company engaged in the production of two products A and B
Product A Rs p.u Product B Rs. p.u
Selling price 1000 2000
Materials (Rs.100 per kg) 200 500
Labour ( RS.6 per hour) 300 600
Variable overheads 100 200

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 Fixed overheads Rs.1, 00,000
If total availability of raw material 4000 kgs and max sales potential of each product
is 1000 units. Find out most profitable product mix.

7. X ltd has manufactured and sold 3 products during 2005 as follows

Product X 20000 units
Product Y 14000 units
Product Z 10000 units
Cost analysis has disclosed as follows
Product X Product Y Product Z
Marginal cost 10 18 16
Listed price 20 30 40
Time taken (hours) 2.5 3 2.5
Fixed cost Rs.2, 00,000
Discount 10%
Due to shortage of lab our, the available hours for the next year are expected to be
only 90000 hours
Suggest a suitable product mix for the next year
 When there is enough demand for all the three products
 When the potential demand is
X 18000 units
Y 10000 units
Z 12000 units

8. The following particulars are extracted from the records of a company

Product A Product B
Sales Rs.100 Rs.120
Consumption of materials 2 kgs 3 kgs
Material cost Rs.10 Rs.15
Direct wages RS.15 RS.10
Direct expenses RS.5 RS.6
Machine hours used 3 hours 2 hours
Overhead expenses
Fixed Rs.5 Rs.10
Variable Rs.15 Rs.20
Direct wages are Rs.5 per hour. Comment on the profitability of each product
(both use the same raw material) when
 Total sales potential in units is limited
 Total sales potential in value is limited
 Raw material is in short supply
 Production capacity (in terms of machine hours) is the limiting factor
Assuming raw material as the key factor, availability of which is 10000 kgs and
maximum sales potential of each product being 3500 units, find the product mix
that gives maximum profit.

9. Udyog ltd., which is engaged in 3 lines furnishes the following data for 2005-06

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 Line A Line B Line C
Selling price per unit (Rs.) 100 75 50
PV ratio (%) 10 20 40
Maximum sales potential 40000 25000 10000
(units)
Raw materials content as a 50 50 50
percentage of variable cost
The fixed cost is estimated at Rs.6, 80,000. The company uses a single raw
material in all the three lines. The raw material is in short supply and the
company has a quota of the supply of Rs.18, 00,000 worth of materials for the
year 2005-06
 Set a product mix which will give maximum overall profit, keeping in
view, shortage of materials supply
 Compute the maximum profit

10. XY ltd. is manufacturing three household products A, B, C and selling them in

competitive market. Details of current demand, selling price and cost structure
are given below

Product A Product B Product C

Expected demand (units) 10000 12000 20000
Selling price per unit Rs. 20 16 10
Variable cost per unit Rs.
Direct materials (RS.10/ kg) 6 4 2
Direct labour (Rs.15 per hour) 3 3 1.50
Variable overheads 2 1 1
Fixed overhead per unit (Rs.) 5 4 2
The company is frequently affected by acute scarcity of raw material and high
labour turnover. During the next period it is expected to have one of the
following situations
 Raw materials available will be only 12100 kg
 Direct labour hours available will be only 5000 hours
 It may be possible to increase sales of any one product by 25% without
any additional fixed costs buy by spending Rs.20, 000 on advertisement.
There will be no shortage of materials or labour.
Suggest the best production plan in each case and the resultant profit that the
company would earn according to your suggestion.

11. A company produces three products. The cost data are as under
Product A Product B Product C
Direct material Rs.64 Rs.152 Rs.117
Direct labour
Department 1@ Rs.5 per 18 hours 10 hours 20 hours
hour
Department 2 @ Rs.6 5 hours 4 hours 7 hours

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 per hour
Department 3 @ Rs.4 10 hrs 5 hrs 20 hrs
per hour
Variable overheads Rs.16 Rs.9 Rs.21
Fixed overheads Rs.4, 00,000 per annum
The budget was prepared at a time when the market was sluggish. The budgeted
quantities and selling prices are as under.
Product Budgeted Quantity Selling price / unit
A 9750 270
B 7800 280
C 7800 400
Later the market improved and the sales quantities could be increased by 20% for
product A and 25% each for products B and C. The sales manager confirmed that
the increased quantities could be achieved at the prices originally budgeted. The
production manager stated that the output couldn’t be increased beyond the
budgeted level due to limitation of direct labour hours in department 2
Required
 Present a statement of budgeted profitability
 Set optimal product mix and calculate the optimal profit

12. A manufacturer has three Orient Express sell three brands of its products in the
Middle East. The market for different price segments are given below
Brand name Selling price per unit Market demand (units)
Juveline 6.00 1,00,000
5.50 1,20,000
Adult 5.00 2,00,000
4.75 2,20,000
Aged 5.50 80,000
5.25 96,000
The capacity to pack and export is presently restricted to 400000 units per month.
The variable costs of production are as follows
Rs.per unit
Juveline Adult Aged
Raw material 2.10 1.50 1.40
Packing materials 1.60 1.00 1.00
Labour and expense 0.62 0.58 0.57
Trade discount is allowed @ 6% of selling price of which 1% is allowed to be
retained by the Overseas agent. Variable distribution and handling charges
amount to Rs.12 per carton containing 50 units each. Export duty is payable @
5% ad valorem. Export incentives is considered @ 30% of net selling price after
considering discount allowed to Overseas Agency.
Considering the capacity constraint, calculate the optimum product mix.

13. The Royal industries manufactures three different plastic products from a single
raw material and common processing budgeted data for 2005 are give below:

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 The production costs identified with the individual products are only the costs
incurred split off point
A B C Joint costs
Output (units) 45000 30000 15000
Selling price
per unit Rs.6 Rs.12 Rs.18
Direct 3,00,000
materials Rs.24, 000 Rs.36, 000 Rs.30, 000
Direct labour 1,50,000
Variable mfg Rs.12, 000 Rs.18, 000 Rs.12, 000
o/h 48,000
Fixed mfg Rs.18, 000 Rs.30, 000 Rs.24, 000
O/H 96,000

The sales manager has suggested the following sales mix of products
Product A 30000 units
Product B 40000 units
Product C 20000 units
This proposed sales mix would add Rs.1, 00,000 to the total joint processing cost.
Comment on the economic feasibility of the proposed mix.

14. On the basis of the following information in respect of an engineering company,

what is the product mix, which will give you the highest profit attainable? Go
you recommend overtime working up to a maximum of 15000 hours at twice the
normal rates? (Ignore overheads)
Product A p.u Product B p.u Product C p.u
Raw materials (in kgs) 10 6 15
Labour hours @ Re.1 per hour 15 25 20
Selling price (Rs) 125 100 200
Maximum production possible 6000 4000 3000
(units)
One lakh kgs of materials are available at Rs.10 per kg. Maximum production
hours are 1,84,000 with facility for a further 15000 hours on overtime basis twice
the normal rate.

15. Novelties Ltd. seeks your advice on production mix in respect of the three
products Super, Bright an[d Fine. You have the following information data of
standard costs per unit
Super Bright Fine
Direct materials 320 240 160
Variable overhead 16 40 24
Direct labour
Department Rate per hour Super (hours) Bright (hours) Fine (hours)
(Rs)
A 8.00 6 10 5
B 1.00 6 15 11

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 You are also to note that there is a constraint on supply of labour in Department A
and its manpower cannot be increased beyond its present level.
Suggest the best production and sales mix from the standpoint of maximum
profitability. Prepare statements setting out the profit resulting from the budgeted
production and the best alternative suggested by you.
16. The board of directors of Fortune Ltd., manufacturing three products A, B and C
have asked your advice on the production mixture of the company.
 You are required to prepare a statement of the most profitable mixture of
the products to be made and sold. The statement should show:
a. The profits expected on the current budgeted production
b. The profits, which could be expected if the most profitable mixture
was produced.
 You are also required to invite the director’s attention to any problems,
which are likely to arise if the mixture in (b) above were to be produced.
Product A Product B Product C
Data for standard cost per unit:
Direct materials (Rs.) 10 30 20
Variable overheads (Rs.) 3 2 5
Direct labour:
Dep 1 (Rs.0.50 per hour) 28 hrs 16 hrs 30 hrs
Dep 2 (Rs.1.00 per hour) 5 hrs 6 hrs 10 hrs
Dep 3 (Rs.0.50 per hour) 16 hrs 8 hrs 30 hrs
Data for current budget
Production p.a (units) 10000 5000 6000
Selling price per unit (Rs.) 50 68 90
Max. Possible sales (units) 12000 7000 9000

Fixed overheads per; year Rs.2, 00,000

However the type of labour required in Department 2 is in short supply and it is
not possible to increase that manpower of this department beyond its present
level.

17. Sum Toys ltd. Manufactures and sells children’s toys of high quality over an
extensive market, utilizing the services of skilled artisans who are paid at an
average rate of Rs.15 per hour. The total number of skilled labour hours available
in a year is only 14000. The details of planned production for 20054-06 estimated
cost and unit-selling prices are given below.
Toy Production Direct Direct Fixed Selling
planned materials labour overheads price per
(units) Rs. Rs unit Rs
A 3000 20 10 15 70
B 4000 24 12 18 92
C 4000 32 12 18 95
D 3000 40 16 24 110
E 2400 60 20 30 180
Variable overhead cost amount to 50% of direct labour cost

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 The company has estimated the following maximum and minimum demand for
each product
Toy Maximum (units) Minimum (units)
A 5000 1000
B 6000 1000
C 6000 1000
D 4000 500
E 4000 500
 What is the estimated profit for the year 2005-06 as per the company’s
production plan?
 Do you agree with the said plan? If not, what would be the plan for
maximum profit?
 What is the estimated profit as per the plan suggested by you

18. BVX ltd manufactures three garden furniture products chairs, benches and tables.
The budgeted unit cost and resource requirements f each of these items is detailed
below
Chair Bench Table
Timber cost 5.00 15.00 10.00
Direct labour cost 4.00 10.00 8.00
Variable overhead cost 3.00 7.50 6.00
Fixed overhead cost 4.50 11.25 9.00
16.50 43.75 33.00
Budgeted volumes per
annum 4000 2000 1500
Selling price Rs. 20 50 40
 These volumes are believed to equal the market demand for these products
 The fixed overhead costs are attributed to the three products on the basis
of direct labour hours
 The labour rate is Rs4.00 per hour
 The cost of the timber is Rs.2 per square meter
The products are made from special timber. A memo from the purchasing
manager advises you that because of a problem with the supplier, it is to be
assumed that this special timber is limited in supply to 20000 square meters per
annum
The sales director has already accepted an order for 500 chairs, 100 benches and
150 tables, which is not supplied, would incur a financial penalty of Rs.2000.
These quantities are included in the market demand estimates above
Requirements:
Determine the optimum production plan and state the net profit that this would
yield per annum’
Calculate and explain the maximum prices, which should be paid per square
meter n order to obtain extra supplies of the timber

19. A company engaged in the manufacture o sophisticated products uses high-grade

raw materials, which are in short supply. During the year 2004 the company

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earned a profit of 12% before interest and depreciation on a turnover of Rs.10
crore. Interest and depreciation, which are fixed, amounted to Rs.75 lakhs and
Rs.50 lakhs respectively. The product mix was as under
Product PV ratio Raw materials as % Of turnover to
% to sales value total turnover
A 30% 40 30
B 40% 50 20
C 25% 36 50
During the year the prices of raw materials are expected to increase by 10%. The
company has been able to make arrangements for the procurement of raw
materials of a total value of Rs.561 lakhs at 2005 prices. The sales potential of
each product can be increased in 2005 by 50% of 2004 sales.
Set the optimal product mix for 2005.