Consider the relationship between TEC and O'Neill with unlimited, but expensive, reactive capacity. Recall that TEC is willing to give O'Neill a midseason replenishment but charges O'Neill a 20 percent premium above the regular wholesale price of $110 for those units. Suppose TEC's gross margin is 25 percent of its selling price for units produced in the first production run. However, TEC estimates that its production cost per unit for the second production run (any units produced during the season after receiving O'Neill's second order) is twice as large as units produced for the initial order. Wetsuits produced that O'Neill does not order need to be salvaged at the end of the season. With O'Neill's permission, TEC estimates it can earn $30 per suit by selling the extra suits in Asian markets.
a. What is TEC's expected profit with the traditional arrangement (i.e., a single order by O'Neill well in advance of the selling season)? Recall that O'Neill's optimal newsvendor quantity is 4,101 units.
b. What is TEC's expected profit if it offers the reactive capacity to O'Neill and TEC's first production run equals O'Neill's first production order? Assume the demand fore- cast is normally distributed with mean 3,192 and standard deviation 1,181. Recall, O'Neill's optimal first order is 3,263 and O'Neill's expected second order is 437 units.
c. What is TEC's optimal first production quantity if its CEO authorizes its production manager to choose a quantity that is greater than O'Neill's first order?
d. Given the order chosen in part c, what is TEC's expected profit?