After some linear regression analysis, you have arrived at the following simple model of the demand D for a product as a function of its price P:
D = 12000 - 160P.
That is, if you distributed the product for free, your customers would still only want 12,000 units per month. For each dollar you increase the price, you estimate that demand falls by 160 units per month.
Your unit variable cost is $20 per unit. The facility that produces the product has a capacity of up to 10,000 units per month. The lease and utilities for the facility amount to $30,000 per month, which may only be avoided by making zero units (however, it is not clear that if you gave up the lease, you would be able to lease the facility again later).
Suppose you do not want to keep any inventory of the product, but instead produce an amount exactly equal to customer demand each month. What price and production quantity will maximize your profits?
A colleague suggests that the $20 per unit variable cost is not the "true" cost, because you should also include the cost of facility. He proposes to do so by adding a facility charge of $ 3/unit = (30,000 $/month) / (10,000 units/month) to the unit cost, for an adjusted unit cost of $23/unit. Recalculate the "optimal" price using this adjusted unit cost, and show that it is higher than the price in part (a), and results (at least according to the model) in lower actual profit per month.