A new-car dealer expects to sell 36 of a particular model car in the next year. It costs $850 per year to keep an unsold car on the lot. Fixed costs associated with preparing, processing, and...

A new-car dealer expects to sell 36 of a particular model car in the next year. It costs $850 per year to keep an unsold car on the lot. Fixed costs associated with preparing, processing, and receiving a single order from Detroit total $230 per order.

a. Using the information provided, express the yearly inventory expense E = E(Q) as a function of Q, the number of automobiles included in a single order.

b. What is the yearly inventory expense if 3 cars at a time are ordered?

 c. How many cars at a time should be ordered to make yearly inventory expenses a minimum?

d. Using the value of Q you found in part c, determine how many orders to Detroit will be placed this year.

 e. What is the average rate of increase in yearly inventory expense from the number you found in part c to an order of 2 cars more?