Zek Ltd assembles heavy industrial switchboxes. Hitherto, Zek Ltd has assembled only one type, but recently a decision was made to expand the product range into two types. The following data pertains to each switchbox:

[40]

Selling price per unit Variable costs per unit:

- Direct materials

- Direct labour

- Manufacturing overhead

Specific fixed costs per day

Existing product Z686 (R)

8 000

6 000 500 500

10 000

New product Z797 (R)

6 800

5 600 400 200

5 000

Zek Ltds total general fixed costs per day amount to R27 000.

The organisation operates its factory 24 hours per day and this

cycle. Each switchbox goes through two processes, namely assembly and testing. The number of units which can be assembled or tested in one operating cycle is as follows:

Assemble Test

Z686 2 6 Z797 6 3

Zek Ltd is limited to 600 assembly hours and 400 testing hours in one operating cycle. Management is anxious to ascertain the following, but are unsure as to how to determine these factors:

1. The most profitable daily (that is, in one operating cycle) production combination.

2. The minimum number of units which should be produced in one operating cycle if

Zek Ltd wishes to achieve a total daily profit of R10 000.

equates to one operating

Required

1.1 Explain why linear programming is appropriate in determining the optimal production solution for Zek Ltd. (3)

1.2 Outline the steps to be undertaken when using the graphic linear programming method. (5)

1.3 Determine, using graphic linear programming, the production combination for Zek Ltd

which maximises daily profit. (Draw the graph in your answer book. Ensure that you label the graph comprehensively and clearly.) (17)

1.4 Solving algebraically, verify your answer in (C). (2)

1.5 Calculate the production mix which will achieve the desired daily profit of R10 000.

(8)

1.6 Outline some key assumptions and limitations pertaining to linear programming.

QUESTION ONE [40] Zek Lid assembles heavy industrial swichboxes. Hitherto, Zek Lid has assembled only one type, but recently a decision was made to expand the product range into two types. The following data pertains to each switchbox: Zek Ltt's total general fleed costs per day amount to R27 000 . The organisation operates its tactory 24 hours per day and this equates to one operating cycle. Each swichbox goes through two processes, namely assembly and testing. The number of units which can be assembled or tested in one operating cycle is as follows: Zek Ltd is imiled to 600 assembly hours and 400 testing hours in coe operating cycle. Management is arxious to ascertain the following, but are unsure as to how to determine these factors: 1. The most profitable daily (that is, in one operating cycle) production combination. 2. The minimum number of units which should be produced in one operating cycle if Zok Ltd wishes to achieve a total daly profit of R10 000 . Required 1.1 Explain why linear programming is appropriate in determining the optimal production solution foe Zek Lid. 1.2 Outine the steps to be undertaken when using the graphic linear programming method. (5) 1.3 Dotermine, using graphic linear programming, the production combination for Zek Lted which maximises dally profit. (Draw the graph in your answer book. Ensure that you label the graph comprehensively and cleady.) (17) 1.4 Solving algebraically, wenty your answer in (C). (2) 1.5 Calculate the production mix which will achieve the desired daily profit of R10 000. (8) 1.6 Outhe some key assumptions and limitations pertaining to linear programming