Doug is concerned with setting a correct production level. He can produce 1000 u

Question

Doug 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 50% chance of high demand (2500 units) and a 20% chance of low demand (750 units) and a 30% chance of average demand (1200 units). Each unit costs $7.50 to produce and sells for $10. 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).

What is the expected value of profit if you make a decision based on the expected value of profit? Indicate your answer, rounded to two decimal places (i.e. 111.01).

Explanation / Answer

DOug will produce what he chooses either its 1000 units or 2000 units,

Pr( 1000 units producton) = Pr(200 units production) = 0.5

Pr(High Demand) = 0.50

Pr(low demand) = 0.20

Pr(average demand) = 0.30

Let say he produced 1000 units so her can sel at max 1000 units and it is applicable for 2000 units also.

Profit on one unit of production = $ 2.5

Expeted value of profit = Profit in certain case * Pr(Production level) * Pr (demand status) * 2.5$

= 0.5 * 0.2 * [(750 * 10 - 1000 * 7.5) + (750 * 10 - 2000 * 7.5)] + 0.5 * 0.3 * [(1000 * 10 - 1000 * 7.5) + (1200 * 10 - 2000 * 7.5)] + 0.5 * 0.5 * [(1000 * 10 - 1000 * 7.5) + (2000 * 10 - 2000 * 7.5)]

= -$ 750 - $ 75 + $ 1875

= $1050

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