This assignment will not be collected for a grade
as it is the last assignment immediately prior to the exam.
Problems LP1, LP2, LP3, LP4, and B.10 are to be solved by the manual graphical method using an iso-Z line to either maximize or minimize the objective function whichever is appropriate.
LP1 The Really Big Shoe (RBS) is a manufacturer of basketball and football shoes. Ed must decide the best way to spend advertising resources. Each football team sponsored requires 120 pairs of shoes. Each basketball team requires 32 pairs of shoes. Football coaches receive $300,000 for shoe sponsorship and basketball coaches receive $1,000,000. Ed’s promotional budget is ...view middle of the document...
1 g |0.6 g |2000 g/month |
| |Bottling |1 bottle |1 bottle |6000 bottles/month |
| |Market |1 bottle | |4000 bottles/month |
Min z = x1 + 2 x2
st. x1 + 3 x2 >= 90
8 x1 + 2 x2 >= 160
3 x1 + 2 x2 > = 120
x2 = 0
Ans = x1 = 25.71, x2 = 21.43, z = 68.57
This is the slack time of the year at Iota Inc. The company would actually like to shut the plant down, but if the they do, the highly skilled and trained core employees would likely be picked up by a competing company which is undesirable. The company could keep the core employees busy by producing (at a minimum) 10,000 round tables per month, or by making 20,000 square tables per month, or some ratio thereof. Iota does however have a standing contract to produce 5,000 square tables per month. Handling and storage costs per round tables are $10 and per square table are $8. Formulate a linear program to minimize the costs. Hint: Let x1 = the thousands of round tables per month and let x2 = the thousands of square tables per month. Solve graphically to determine the optimal quantities and cost. Ans = x1 = 7500, x2 = 5000, z = 115,000
B.10 Page 709 Ans = 10 alpha, 24 beta, z = 55200
The following problems are to be solved using a spreadsheet.
WARNING: DO NOT GO TO THE COMPUTER LAB WITHOUT HAVING FORMULATED THE LINEAR PROGRAMS! The software only can solve a formulated linear program. IT CANNOT NOR CAN IT EVER FORMULATE THE LP FOR YOU. THIS YOU MUST HAVE DONE BEFORE ENTERING THE LAB. But it does one excellent job of solving them for you. The software performs the Simplex method to solve the linear program. Knowing the intricacies of the Simplex method won’t make you a better manager or investor, but having an understanding the generated solution certainly can!
LP5 Polly makes fine clothing for big and tall men. A few years ago, Polly entered the sportswear market with the Sunset line of shorts, pants and shirts. Management wants to make the amount of each product that will maximize profits. Each type of clothing is routed through two departments A and B. The following table describes the relevant data for each product.
| |Product |Dept A |Dept B |Material (yd) |
| |Shirt |2 |1 |2 |
| |Shorts |2 |3 |1 |
| |Pants |3 |4 |4 |
Department A has 120 hours of capacity, department B has 160 hours of capacity, and 90 yards of material are available. Each shirt contributes $10 to profit and each pair of shorts $10 and each pair of pants...