I suggest you use an Excel sheet with one question on each tab. See below with the question 4 used as an example :
1. Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 52 units of synthetic fiber, requires 28 hours of production time, and needs 22 units of foam backing. Each roll of Grade Y carpet uses 45 units of synthetic fiber, requires 30 hours of production time, and needs 16 units of foam backing.
The profit per roll of Grade X carpet is $205 and the profit per roll of Grade Y carpet is $155. In the coming production period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility. This means that instead of using the = or ≤ sign in the constraint you should use the ≥ sign.). The company has 1500 units of foam backing available for use.
Develop and solve a linear programming model for this problem.
:
Let X = the number of rolls of Grade X carpet to make
Let Y = the number of rolls of Grade Y carpet to make
How much of each carpet X and carpet Y be produced to maximize profits? Note: Round down if necessary.
What is the profit?
Note: You can submit your Excel Sheet with the answer if you want to.
2. Canning Transport is to move goods from three factories to three distribution centers. Information about the move is given below. Note: This is a transportation problem.
a.
Source
Supply
Destination
Demand
A
300
X
200
B
200
Y
275
C
250
Z
275
Shipping costs are:
Destination
Source
X
Y
Z
A
4
3
6
B
10
11
10
C
6
7
5
a. What is the total cost?
. What should be shipped from each supply node to each destination node.
Note: You can use the Excel sheet to provide your answer.
3. RVW (Restored Volkswagens) buys 30 used VW's at each of two car auctions each week held at different locations. It then transports the cars to repair shops it contracts with. When they are restored to RVW's specifications, RVW sells 20 each to three different used car lots. There are various costs associated with the average purchase and transportation prices from each auction to each repair shop. Also there are transportation costs from the repair shops to the used car lots. RVW is concerned with minimizing its total cost given the costs in the table below.
Repair Shops
Used Car Lots
S1
S2
L1
L2
L3
Auction 1
500
400
S1
350
400
600
Auction 2
550
350
S2
450
750
550
c. What is the total cost?
d. What should be shipped?
Note: You can use the Excel sheet for your answer.
4. The LP model and output below represent a problem whose solution will tell a specialty retailer how many of four different styles of um
ellas to stock in order to maximize profit. It is assumed that every one stocked will be sold. The variables measure the number of women's (X1), golf (X2), men's (X3), and folding um
ellas (X4), respectively. The constraints measure storage space in units (Constraint 1), special display racks (Constraint 2), demand (Constraint 3), and a marketing restriction (Constraint 4), respectively. There is nothing that you need to solve for this problem. All questions below can be answered by the output.
MAX 5 X1 + 7 X2 + 6 X XXXXXXXXXXX4
SUBJECT TO
1) 2 X1 + 3 X2 + 3 X3 + X4 <= 120
2) 1.5 X1 + 2 X2 <= 54
3) 2 X2 + X3 + X4 <= 72
4) X2 + X3 >= 12
Answer Report (Note the order of the constraints. Excel placed them out of order so make sure you see that Constraint 1 is the second constraint listed and constraint 4 is the first constraint listed).
Sensitivity Report (See note above regarding order of constraints).
END
Use the output to answer the questions.
a.
How many women's um
ellas (X1) should be stocked?
b.
How many golf um
ellas (X2) should be stocked?
c.
How many men's um
ellas (X3) should be stocked?
d.
How many folding um
ellas (X4) should be stocked?
e.
How much space is left unused?
f.
How many racks are used?
g.
By how much is the marketing restriction exceeded?
h.
What is the total profit?
i.
By how much can the profit on women's um
ellas increase before the solution would change?
j.
To what value can the profit on golf um
ellas increase before the solution would change?
k.
By how much can the amount of space increase before there is a change in the dual price?
l.
You are offered an advertisement that should increase the demand constraint from 72 to 86 for a total cost of $20. Would you say yes or no? Why?
m.
If Storage Space (Constraint 1) is increased by 12 and Special display racks (Constraint 2) is decreased by 12, would the problem need to be rerun? Why?
Extra Credit: 5 points
Write the following constraint in co
ect form with a number for the RHS.
Supervisory labor hours (SL) can be no more the one-fourth the amount of Factory Labor (FL) hours.