Linear Programming Assignment
A company manufactures three products, each of which utilizes some capacity in three manufacturing departments—assembly, inspection, and packing. The capacity requirements per unit of product in hours are shown in the table.
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Product |
Production Time in Hours per Unit |
||
|
|
Assembly |
Inspection |
Packing |
|
A B C |
0.30 0.50 0.40 |
0.10 0.08 0.12 |
0.06 0.04 0.05 |
Available capacities per week are 1800 hours of assembly time, 800 hours of inspection time, and 700 hours of packing time. The profit per unit sold is $0.20 for A, $0.15 for B, and $0.10 for C. All products produced can be sold for this profit. What should be the production rate per week for each product in order to maximize profits?
LP Problem 2
Two products are made by blending three raw materials according to these specifications:
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|
Material |
Price/Pound |
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|
Product |
|
|
||
|
|
1 |
2 |
3 |
|
|
|
|
|
|
|
|
A |
10% |
≥30% |
≤80% |
$12.00 |
|
B |
≥30% |
≥20% |
≤60% |
$15.00 |
|
Mat’l Avail |
4000 |
6000 |
10,000 |
|
|
Mat’l Cost |
$3.00 |
$2.00 |
$1.00 |
|
All manufacturing costs, other than material, are assumed to be $2.00 per pound regardless of the product or blend. Determine the blend to use for each product and the quantities of each to produce each week to obtain maximum profits.
LP Problem 3
A plant makes three products, A, B, and C. The following data describe the production planning problem:
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Profit Minimum per Weekly Product Piece Requirements |
Processing Time in Hours per Piece |
||||
|
|
Lathe Dept. |
Milling Dept. |
Grinding Dept. |
Inspection Packing |
|
|
A $20 100 pieces |
0.2 |
0.5 |
0.1 |
0.02 |
0.05 |
|
B 18 180 |
0.1 |
.... |
0.3 |
0.02 |
0.06 |
|
C 21 75 |
0.3 |
0.07 |
0.1 |
0.02 |
0.05 |
|
Department Capacity in Hours per Week |
160 |
80 |
80 |
40 |
40 |
For example, products A and C have to be processed through all five departments, while product B would not have to be processed through the milling department.
Determine the weekly production rate for each product that maximizes profit.
LP Problem 4
A manufacturer of fertilizer markets four mixes of lawn fertilizer: 6-8-6, 10-6-4, 12-5-8, 14-5-10. The numbers refer to the percentage by weight of nitrates, phosphates, and potash, respectively, in the product.
Manufacturing is a mixing process whereby the active ingredients are mixed in the proper proportions with inert ingredients, and the mix is then packaged and sold.
For the period being planned, the manufacturer has available 2300 tons of nitrates, 1400 tons of phosphates, and 1800 tons of potash. He has access to a very large supply of the inert ingredients, so that they will not constrain his choice of a production program.
Demand data for the period are shown in the following table:
The company must produce at least the minimum quantity forecast and will not produce an amount greater than the maximum forecast.
The costs per ton of the fertilizer components are the following: nitrates, $200; phosphates, $60; potash, $90; other ingredients, $15. Costs of packaging materials, mixing, bagging, and selling are estimated to be $20 per ton, regardless of the mix.
Determine how much of each product to produce to maximize profit.
LP Problem 5
A company has three plants, all of which make the same product. This product is made to order and the decision problem is to determine at which plant an order should be made. The following orders are to be scheduled into production.
|
Customer |
Order Size |
Shipping Costs per Unit |
||
|
|
|
From Plant 1 |
From Plant 2 |
From Plant 3 |
|
W X Y Z |
700 units 1500 400 500 |
$ 8.00 11.00 6.00 9.00 |
$ 4.00 10.00 12.00 5.00 |
$ 6.00 8.00 7.00 14.00 |
The production costs vary from plant to plant and so does the available capacity:
|
Plant |
Unit Mfg. Cost |
Capacity |
|
A |
$45 |
1000 |
|
B |
$40 |
800 |
|
C |
$50 |
1500 |
Find the minimum-cost production-distribution schedule, assuming that orders can be split among the plants.