A manufacturer of industrial sales has production capacity of 1,000 units per day. Currently, the firm sells production capacity for $10 per unit
At this price, all production capacity gets booked about one week in advance. A group of customers have said that they would be willing to pay $15 per unit if capacity was available on the last day. About ten days in advance, demand for the high-price segment is normally distributed with a mean of 250 and a standard deviation of 100. How much production capacity should the manufacturer reserve for the last day?
What will be an ideal response?
Answer:
Revenue from segment A, pA = $15 per unit
Revenue from segment B, pB = $10 per unit
Mean demand for segment A, DA = 250 units
Standard deviation of demand for segment A, σA = 100 units
CA = NORMINV(1 - pB/pA, DA, σA)
= NORMINV(1 — 10/15, 250, 100)
= 206.9272 ≈ 207 units of capacity
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