Question: Profit 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 by the equation

\(P(p, b)=144 p-3 p^{2}-p b-2 b^{2}+120 b+35\) dollars

1. Find how much the nursery should charge for each type of mulch in order to maximize the weekly profit from the sale of mulch.
2. Explain in detail how the Determinant Test verifies that your result in part \(a\) gives the maximum profit.
3. What is the maximum weekly profit from the sales of these two types of mulch?

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