4. Pacperson, Inc., manufactures two series of computer hardware: Twopack and Threepack. Data concerning selling prices and costs for each unit are as follows:

Two pack Three pack

Selling price R1 000 R1 700

Materials 350 370

Direct labour 210 230

Overhead (80% fixed) 150 200

Gross margin 290 900

Marketing costs (variable) 80 240

Administrative costs (fixed) 60 80

Profit R150 R 580

Management has decided that at least 500 units of Twopack must be manufactured and sold each month. Likewise, at least 150 Three pack models must be manufactured and sold each month.

The company's production facilities are limited by machine capacity in the Assembly Control Section. Each Twopack model requires one quarter hour in the Assembly Control Section. Each Threepack model, however, requires three quarters of an hour in the assembly area. There is a total of 250 available hours per month in the Assembly Control Section. There are no other relevant constraints on production.

Required:

a. What is the appropriate objective function for these two products if management's objective is to maximise profits?

b. What equations would represent the constraints on the profitability from these two products?

c. Given the information in the problem, which product would management prefer to produce to maximise profits?

d. Graph the profit maximisation problem and identify the feasible production region and corner points.

e. What is the optimal production schedule and the optimal contribution margin at that schedule?

f. What is the maximum price management would be willing to pay for one more hour of Assembly Control Section capacity?

g. What is the opportunity cost of each Two pack model? Why?