eomponent searehes and produet eost Retum to problem 8 above. Now suppose Ralph likes to think in terms ofhow many units of the first product, x, to produce and sell. Clearly we require 0 :s x :s 400. Within this range, it should also be clear Ralph would produce as many units of the second produet as possible. This implies, for any such x, the corresponding choice of y would be y = g(x) = min {400 - x; .5(500 - x)}. This implies a total contribution margin of lOx + 12g(x) = lOx + 12[min {400 - x; .5(500 - x)}].

a] Plot this expression, for 0 :s x s 400. Determine the optimal choiee of x.

b] Next, observe this funetion simplifies to lOx + 3,000 - 6x if 0 s x s 300 and lOx

+ 4,800 - 12x if 300 :s x :s 400. Concentrate on the first range. What is the incremental or marginai cost of the first product in this range? Carefullyexplain your answer, in light of the fact this product's contribution margin was rreviously ealeulated as revenue of 40 less variable cost of 30.

c] Why does the cost of the product depend on the decision frame?AppendixLO1