Quantitative Decision Model

The Acme Company produces three products – A, B & C. All products are produced on 1 machine which has 40 available hours (2400 minutes) each week. All products use the same 1 ingredient. This week there is 100 kg of this ingredient available. The cost (including material, use of the machine, and labour) per unit of each product is: $2 for product A, $3 for product B and $2.50 for product C. The machine time required per unit of each product is 4 minutes for product A, 6 minutes for product B and 8 minutes for product C. The amount of ingredient required per unit of each product is: .25kg for product A, .40kg for product B and .3 kg for product C. The selling prices are: $15 per unit of product A, $18 per unit of product B and $17 per unit of product C. Formulate a linear programming model that would allow Acme to maximize its profits under the following restrictions (in addition to the obvious restrictions):

* at least 15 units of each product must be produced

* at least 2 units of product A must be produced for each unit of product B

* no more than 60% of the total number of units produced can be product C

* the total cost of producing product A can be no greater than 70% of the total cost of producing products B and C combined

* the amount of time producing product B must be at least 20% of the total time producing all the products

Max 13A + 15B + 14.5C

s.t.

4A + 6B + 8C ≤ 2400

.25A + .40B + .30C ≤ 100

A ≥ 15

B ≥ 15

C ≥ 15

A - 2B ≥ 0 ← A ≥ 2B

- .6A - .6B + .4C ≤ 0 ← C ≤ .6(A + B + C)

2A – 2.1B – 1.75C ≤ 0 ← 2A ≤ .7(3B + 2.5C)

- .8A +4.8B - 1.6C ≥ 0 ← 6B ≥ .2(4A + 6B + 8C)