Question

in q1, we found an expression for the cost of producing the magicpuppy as a function of units produced. in q2, we found an expression for the demand as a function of the selling price. we have decided to produce exactly the same number of magicpuppies as the demand we anticipate. in other words, we have set our production quantity to be equal to the anticipated demand for our given selling price. write an expression for the cost of producing the magicpuppy as a function of the selling price. use to indicate the selling price in dollars per unit.

Answer 1

To find the cost of producing the 'magicpuppy' as a function of the selling price P, substitute the demand function D(P) into the cost function C(Q) to derive C(D(P)) = (Average cost) * (8 - 0.5P), which expresses production costs in terms of the selling price.

Step-by-step explanation:

To express the cost of producing the 'magicpuppy' as a function of the selling price P, we need to integrate the given production and demand functions. If we previously established a production cost function C(Q) based on quantity Q and a demand function D(P), with P being the selling price per unit, and we have set Q = D(P), our task is to substitute the expression for Q from the demand function directly into the cost function.

The resulting function C(D(P)) will then represent the cost of production as a direct function of the selling price. For instance, if our demand function is D(P) = 8 - 0.5P and our cost function is C(Q) = (Average cost) * Q, by substitution, we derive C(D(P)) = (Average cost) * (8 - 0.5P). This allows us to calculate production costs for any given selling price.