Question

A nursery sells mulch by the truckload. Bark mulch sells for $b per load, and pine straw sells for $p per load. The nursery's average weekly profit from the sale of these two types of mulch can be modeled as

P(p, b) = 140p − 3p² − pb − 2b² + 130b + 25 dollars.

(a) How much should the nursery charge for each type of mulch to maximize the weekly profit from the sale of mulch? (Round your answers to the nearest cent.)

pine straw	$
bark mulch	$

(b) Explain how the Determinant Test verifies that the result in part (a) gives the maximum profit.

Since the determinant of the second partials  matrix is  ---Select--- greater than less than greater than or equal to less than or equal to equal to 0 and the second partial P_pp is  ---Select--- greater than less than greater than or equal to less than or equal to equal to 0, the prices result in a maximum profit.

(c) What is the maximum weekly profit from the sales of these two types of mulch? (Round your answer to the nearest dollar.)
$

Answer 1