a) By an ‘Economic Order Quantity’ we mean quantity Q, which when produced in each order, minimizes.

a) By an ‘Economic Order Quantity’ we mean quantity Q, which when produced in each order, minimizes the total cost C incurredin producing and storing material for certain time period to fulfill a given rate of demand for the material during the period. The material demanded for a firm is 10,000 units per year, the cost price of material is sh. 1 per unit and its cost sh. 25 to make the factory ready for production run of the items, regardless of the number of units ’x’ produced in a run and the cost of storing the material is 12.5 percent per year of the shilling value of average inventory x/2 in hand.

i) Show that C = 10,000 + 250,000/x + x/16. (5marks)

ii) Find the ‘Economic Order Quantity’ and the total cost C corresponding to that. (6marks)

iii) Find the total cost when each order is placed for 2,500 units. (2marks)

b) Differentiatethe functions with respect to x

i)

x 1/x + (log x)x

(4marks)

ii) ²