Question

Simpson’s Shoes expects to sell 315 pairs of a certain running shoe in a year. There is a fixed charge of $140 per order and each pair of shoes cost the store $7. It costs the store $8 to store a pair of shoes for a year.

Find the inventory cost as a function of ONLY the number of shoes/order.

Use methods of Calculus shown recently in class to minimize the inventory costs. Give appropriate units.

x=____________________________

r=____________________________ Work->

Minimum inventory cost_________________Work->

Use methods of Calculus shown recently in class to prove that you have mimimized the inventory cost. State the domainfor the number of shoes/order.

Answer 1

let  the number of pair of shoes/order be x

number of orders

storage costs

reorder costs =cost per order * number of orders

total inventory cost =storage costs+reorder costs

differentiate with respect to x

for critical point ,C'(x)=0

inventory cost is minimum when number of pair of shoes/order is 105

number of orders

Minimum inventory cost is 3045 dollars