Inc., an electronics system integrator, is developing a new product. As mentioned in Q11.4, Solectrics can produce a key component for this product. Solectrics sells this component to Flextrola for $72 per unit and Flextrola must submit its order well in advance of the selling season. Flextrola's demand forecast is a normal distribution with mean of 1,000 and standard deviation of 600. Flextrola sells each unit, after integrating some software, for $131. Leftover units at the end of the season are sold for $50.
Xandova Electronics (XE for short) approached Flextrola with the possibility of also supplying Flextrola with this component. XE's main value proposition is that they offer 100 percent in-stock and one-day delivery on all of Flextrola's orders, no matter when the orders are submitted. Flextrola promises its customers a one-week lead time, so the one-day lead time from XE would allow Flextrola to operate with make-to-order pro- duction. (The software integration that Flextrola performs can be done within one day.) XE's price is $83.50 per unit.
a. Suppose Flextrola were to procure exclusively from XE. What would be Flextrola's expected profit?
b. Suppose Flextrola plans to procure from both Solectrics and XE; that is, Flextrola will order some amount from Solectrics before the season and then use XE during the sell- ing season to fill demands that exceed that order quantity. How many units should Flextrola order from Solectrics to maximize expected profit?
c. Concerned about the potential loss of business, Solectrics is willing to renegotiate their offer. Solectrics now offers Flextrola an "options contract": Before the season starts, Flextrola purchases Q options and pays Solectrics $25 per option. During the sell- ing season, Flextrola can exercise up to the Q purchased options with a one-day lead time--that is, Solectrics delivers on each exercised option within one day--and the exercise price is $50 per unit. If Flextrola wishes additional units beyond the options purchased, Solectrics will deliver units at XE's price, $83.50. For example, suppose Flextrola purchases 1,500 options but then needs 1,600 units. Flextrola exercises the 1,500 options at $50 each and then orders an additional 100 units at $83.50 each. How many options should Flextrola purchase from Solectrics?
d. Continuing with part c, given the number of options purchased, what is Flextrola's expected profit?