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:

Existing product Z$686($R$)$New product Z$797($R$)$

Selling price per unit $80006800$

Variable costs per unit:

$-$ Direct materials $60005600$

$-$ Direct labour $500400$

$-$ Manufacturing overhead$500200$

Specific fixed costs per day $100005000$

Zek Ltd$$s total general fixed costs per day amount to R$27000.$

The organisation operates its factory $24$ hours per day and this equates to one operating

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

Z$68626$

Z$79763$

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 R$10000.$Required

$1\mathrm{.}1$ Explain why linear programming is appropriate in determining the optimal production

solution for Zek Ltd$.(3)$

$1\mathrm{.}2$ Outline the steps to be undertaken when using the graphic linear programming

method. $(5)$

$1\mathrm{.}3$ 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.$)(17)$

$1\mathrm{.}4$ Solving algebraically, verify your answer in $1\mathrm{.}3.(2)$

$1\mathrm{.}5$ Calculate the production mix which will achieve the desired daily profit of

R$10000.(8)$

$1\mathrm{.}6$ Outline some key assumptions and limitations pertaining to linear programming. $(5)$