Question :

A market analysis reveals that unit sales will depend on the price of the computer. At the price of $1000, about 5000 units will be sold, but for every increase (or decrease) of $100, sales will decrease (or increase, respectively) by 1000 units. Maximize Kayos profit next year by finding (a) the optimal price and (b) the optimal number of boards to buy from Apex while still honoring the original contract.

Kayo Computer assembles and sells personal computers. Each computer needs one custom-designed printed circuit board (PCB). Kayo has contracted to buy the PCB's from an outside PCB manufacturer, Apex Manufacturing. The one-year contract stipulates that Kayo pays $200 per board to Apex for up to 2000 PCBs. If the annual order quantity exceeds 2000PCBs, then Apex is obligated to give a discount of $40 per board for the portion beyond 2000 , thus selling them at $160. Kayo can also buy the same PCBs from another manufacturer, TCI Electronics, that offers a lower price of $120 per PCB but asks a one-time payment of $100,000 as a nonrefundable design and engineering fee. Kayo's engineers have determined that Kayo may use PCBs from either of the two manufacturers, or from both in any mixture without any manufacturing cost or compatibility problems. The PCB along with other components are assembled by Kayo into its personal computer. The variable assembly cost of the Kayo personal computer is $450 each with an annual fixed cost of $1,500,000. Kayo sells the assembled computer for $1000 each. At the moment no one is sure how many Kayo computers the company can sell for the next year. Jenny Silk, VP of Finance at Kayo Computer, informs you that this model of Kayo computer will be discontinued after next year and so any one-time fee that might be paid to TCI must be justified base on next year's sales alone. She has asked you to help her evaluate certain economic and legal issues as part of her financial plan for the next year