Native Customs sells two popular styles of hand-sewn footwear: a sandal and a moccasin. The cost to make a pair of sandals is $50, and the cost to make a pair of moccasins is $60. The demand for these two items is sensitive to the price, and historical data indicate that the monthly demands are given by

S = 2000 10P₁ and M = 3500 15P₂ , where S = demand for sandals (in pairs), M = demand for moccasins (in pairs), P₁ = price for a pair of sandals, and P₂= price for a pair of moccasins. To remain competitive, Native Customs must limit the price (per pair) to no more than $160 and $200 for its sandals and moccasins, respectively. Formulate this nonlinear programming problem to find the optimal production quantities and prices for sandals and moccasins that maximize total monthly profit.

Define the decision variables as the following way:

P₁ = price for a pair of sandals, and P₂= price for a pair of moccasins.

1. Define the objective function (3 points)

1. Define the constraints (4 points)

1. Determine an optimal solution (3 points)

P1 = P2 = Profit =