nursery sells mulch by the truckload. Bark mulch sells for $b per load, and pine

Question

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) = 132p ? 3p2 ? pb ? 4b2 + 110b + 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 $ What is the maximum weekly profit from the sales of these two types of mulch? (Round your answer to the nearest dollar.)

Explanation / Answer

we are given

P=132p-3p^2-pb-4b^2+110b+25

(a)

now, we can find partial derivative with respect to p and b

P_p=132-6p-b

P_b=-p-8b+110

now, we can set them to 0

and then we can solve for p and b

132-6p-b=0

-p-8b+110=0

now, we can solve for p and b

p=528/47=11.2

b=946/47=20.1

(b)

now, we can find maximum profit

we can plug p and b

and we get

maximum profit =1971.3.........Answer

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