Answer For Group 0f 2ppl - Assignment2
Answer For Group 0f 2ppl - Assignment2
Answer For Group 0f 2ppl - Assignment2
7-31
Consider the following LP problem:
Maximize profit = 5X + 6Y
subject to
= 2X + Y 120
= 2X + 3Y 240
X, Y 0
a) What is the optimal solution to this problem? Solve it graphically.
b) If a technical breakthrough occurred that raised the profit per unit of X to $8,
would this affect the optimal solution?
c) Instead of an increase in the profit coefficient X to $8, suppose that profit was
overestimated and should only have been $3. Does this change the optimal
solution?
Answer
Maximize profit = 5X +6Y
Subject to
2X + Y < = 120
2X + 3Y < = 240
X, Y>=0
From the graph, corner points are (0, 80), (30, 60) and (60,0)
Profit P = 5X + 6Y
P (0, 80) = 5(0) + 6(80) = 480
P (30, 60) = 5(30) + 6(60) = 510
P (60, 0) = 5(60) + 6(0) = 300
Maximum profit is at X = 30 and Y = 60.
Maximum profit is 510.
b) If a technical breakthrough occurred that raised the profit per unit of X to $8, would
this affect the optimal solution?
Profit P = 8X + 6Y
P(0,80) = 5(0) + 6(80) = 480
P(30,60) = 8(30) + 6(60) = 600
P(60,0) = 8(60) + 6(0) = 480
Maximum profit is at X = 30 and Y = 60.
Maximum profit is 600 no change in optimal solution. Optimal solution occurs at X = 30
and Y = 60.
7-16
A candidate for mayor in a small town has allocated $40,000 for
last-minute advertising in the days preceding the election. Two
types of ads will be used: radio and television. Each radio ad
costs $200 and reaches an estimated 3,000 people. Each
television ad costs $500 and reaches an estimated 7,000 people.
In planning the advertising campaign, the campaign manager
would like to reach as many people as possible, but she has
stipulated that at least 10 ads of each type must be used. Also,
the number of radio ads must be at least as great as the number
of television ads. How many ads of each type should be used?
How many people will this reach?
10-18
An air conditioning manufacturer produces room air conditioners at plants in Houston,
Phoenix, and Memphis. These are sent to regional distributors in Dallas, Atlanta, and
Denver. The shipping cost: vary and the company would like to find the least-cost way
to meet the demands at each of the distribution centres. Dallas needs to receive 800 air
conditioners per month, Atlanta needs 600, and Denver needs 200. Houston has 850 air
conditioners available each month. Phoenix has 650 and Memphis has 300. The shipping
cost per unit from Houston to Dallas is $8, to Atlanta is $12 and to Denver is $10. The
cost per unit from Phoenix to Dallas is $10, to Atlanta is $14 and to Denver is $9. The
cost per unit from Memphis to Dallas is $11, to Atlanta is $8, and to Denver is $12. How
many units should be shipped from each plant to each regional distribution centre?
What is the total cost for this?
To
Dallas
Atlanta
Dummy
Warehouse
Denver
From
8
12
1
0
14
1
2
Houston
800
Phoenix
50
10
550
11
800
650
50
8
Memphis
X
850
300
X
600
200
1600
(need
demand)
1800
(supply)
=$ 16,950
Total cost is $ 16,950