QUESTION $3$

It is a requirement that you complete the module Industrial Engineering Practice I and II before you can graduate. Your brother owns a hardware store, and on the occasions, you have worked in the store you have noticed his business experience problems with inventory holding. You offered your assistance in solving some of the inventory problems. During your observations, you determine the annual demand for number six screws is $110000.$ For the purpose of the Work Integrated Learning exercise, your brother made you responsible for all purchases. After studying previous records, you estimate the ordering cost to be R$20$ every time the business places an order for the screws. Furthermore, you estimate that the cost of carrying one screw in inventory for a year is one$-$half of one cent. Observing the process over time, you determine it takes approximately $8$ working days for an order of number six screws to arrive once you place an order. The demand for number six screws is constant, and on average, you observe the store sells $600$ of these screws each day. You believe stockouts can be eliminated if the screws are ordered at the correct time. Your brother is unhappy with the number of orders you ace for the screws. He believes orders should be placed twice a year. You are required to:

$3\mathrm{.}1$ Through the application of the correct equation, compute the number of screws to be ordered at a time if you wish to minimise total inventory cost.

$3\mathrm{.}2$ Through the application of the correct equation, compute the number of orders to be placed annually as well as the annual ordering cost.

$3\mathrm{.}3$ Through the application of the correct equation, compute the average inventory as well as the annual holding cost.

$3\mathrm{.}4$ Through the application of the correct equation, compute the reorder point $($ROP$).$

$3\mathrm{.}5$ If you adhere to the policy prescribed by your brother, how much how much more would this cost every year over the policy you developed? If only two orders were placed each year, what effect would this have on the ROP?

$[25]$

PRDEAPS$/2024$

QUESTION $4$

A friend of yours is selling handcrafted objects at craft markets in your hometown. He requested your assistance in determining whether it will be possible to have a more profitable business. You undertook an investigation and found his variable cost to be R$40$ each. The selling price of the objects is R$70.$ The cost of renting a booth at the craft market is R$170.$ He further informed you that he is attempting to identify a new supplier that will reduce his variable cost of production to R$35$ per unit. Assisting him you are required to:

$4\mathrm{.}1$ Calculate the break$-$even point for the existing position.

$4\mathrm{.}2$ If the negotiations for a new supplier are successful, calculate the new break$-$even point.

$[14]$