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 form the sale of these two types of mulch can be modeled by the equation dollars. To the nearest dollar, what is the maximum weekly profit from the sales of these two types of mulch?
A) $2,635
B) $3,559
C) $1,734
D) $6,372
E) $10,524

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 form the sale of these two types of mulch can be modeled by the equation  dollars. To the nearest dollar, what is the maximum weekly profit from the sales of these two types of mulch?
A) $2,635 
B) $3,559 
C) $1,734 
D) $6,372 
E) $10,524

Quizplus · Accepted Answer

To find the maximum weekly profit, we need to find the maximum value of the given equation. To do this, we can take the derivative of the equation with respect to b and p, set them equal to 0, and solve for b and p.

∂(Profit)/∂b = 3000 - 515b - 205p = 0 
∂(Profit)/∂p = 5000 - 205b - 327p = 0

Solving these two equations gives us b ≈ 9.932 and p ≈ 15.168.

Plugging these values back into the original equation gives us the maximum weekly profit:

Profit = 3000b + 5000p - 205b^2 - 327p^2 - 310bp 
Profit ≈ $3,559

Therefore, the best choice is B.

A Nursery Sells Mulch by the Truckload