QUESTION 3: Linear Programming Formulation (33 points)

Harris Tools has been very successful with its JetSet tool line. There are three tools which Harris sells under the JefSet label: framises, smafises and ababa wheels. Relevant data for the three products is given below:

Product	Framis	Smafis	Ababa Wheel	Available
Revenue/unit	120	150	80
Metal used Per unit (kilos)	4	10	3	1000 kilos
Plastic used per unit (kilos)	8	8	3	1200 kilos
Labour per unit (hours)	5	8	5	800 hours

The cost for resources is $3 per kilo for metal, 6$ per kilo for plastic, and $4 per hour for labour. In addition, at least 50 framises must be produced to service a recently signed contract. Harris wants to maximize profit from its JetSet products. Profit per unit for each product is computed as the difference between revenue per unit and costs of metal, plastic and labour.

An algebraic formulation is as follows:

Let F, S and A be the number of framises, smafises and ababa wheels produced.

Maximize 40F + 40S + 33A

subject to

4F + 10S + 3A 1000

8F + 8S + 3A 1200

5F + 8S + 5A 800

F 50

F, S, A 0

Each formulation question below is independent of the others; this means that when you are answering a part, ignore the previous parts. In (b) to (f) the formulation is altered. You may either write out a complete formulation for the altered problem, or better yet, just clearly state exactly what changes need to be made in the above formulation.

1. Show exactly how the profit per unit of $33 for ababa wheels is computed. (2 points)

2. The revenue per unit for framises has decreased to $115. How does the formulation change? (2 points)

c. The cost per hour for labour has decreased to $3 per hour. How does the formulation change? (2 points)

4. At least 30% of the total number of units produced must be Smafis. How does the formulation change? (3 points)