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Homework answers / question archive / Adam is concerned with setting a correct production level
Adam is concerned with setting a correct production level. He can produce 1000 units or 2000 units, and regardless of demand, will produce what he chooses, either 1000 or 2000 since he must produce this before realizing demand. Regardless of production, there is a 40% chance of high demand (2500 units) and a 25% chance of low demand (750 units) and a 35% chance of average demand (1200 units). Each unit costs $8.00 to produce and sells for $11. He can only sell the minimum of either demand or production (since he can't sell what he doesn't make and can't sell what isn't demanded). Which production decision should he make, based on expected value of profit?
Let's start by computing the expected demand.
Expected demand = Sum of probability of demand * quantity demanded
Expected demand = 40% * 2,500 + 25% * 750 + 35% * 1,200
Expected demand = 1,607 units (we cannot sell half a unit so we always round down)
If Adam produces 1,000 units, his expected profit will be:
Expected Profit = Units sold * Unit price - Units produced * Unit cost
= 1,000 * 11 - 1,000 * 8
=$3,000
If Adam produces 2,000 units, his expected profit will be:
Expected Profit = Units sold * Unit price - Units produced * Unit cost
= 1,607* 11 - 2,000 * 8
=$1,677
Naturally, Adam will select the 1,000 unit production level in order to maximize profit. His expected profit is thus $3,000.
