Question $1(31$ marks$)$

Joan W Wrong Supermarket sells one of its products for $$250$ that includes a mark$-$up of $25\%.$ The annual cost of holding inventory is $0\mathrm{.}5\%(\frac{1}{2}\%)$ per annum. For ordering, an employee is paid a rate of $$10$ per hour to place each order. The product requires $0\mathrm{.}05$ kilogram of raw material. The company sells $200,000$ of this product annually and none is left in inventory at the end of each period. The nomal time to place an individual order is five $(5)$ hours. Currently, the company orders five times per year.

However, management was told that if the orders varied to higher levels, the company stands to benefit from quantity discounts. A discount of $2\mathrm{.}5\%$ is to be received for orders of $250$ kilograms exceeding the current lot size. While, a discount of $5\%$ is to be received for orders of $500$ kilograms exceeding the current lot size and $10\%$ if the current lot size is doubled. The material is currently bought from its supplier for $$200$ per kilogram

Required:

a$.$ Calculate the total cost based on the EOQ.

$[8$ marks$]$

b$.$ Calculate the total cost based on the current policy.

$[4$ mark$]$

c$.$ What is the optimal order quantity?

$[13$ marks$]$

d$.$ Explain three $(3)$ assumptions of EOQ, saying why they are not practical.

$[6$ marks$]$