Question

Native Customs sells a popular style of hand-sewn sandal footwear. The cost of making a pair of sandals is $18. The demand for an item is sensitive to the price, and historical data indicate that the monthly demands are given by D(P)= 400 − 10P where D(P) = demand for sandals (in pairs) and P = price for a pair of sandal. To remain competitive, Native Customs must limit the price (per pair) to no more than $35. Formulate this nonlinear programming problem to find the optimal price for sandals that maximize total monthly profit and monthly profit.

Define the decision variables

Answer 1

To formulate the nonlinear programming problem for Native Customs, the decision variables are price (P) and demand (D(P)). The objective is to maximize Profit(P) subject to the pricing constraint of no more than $35 per pair and the given cost of production.

Step-by-step explanation:

The student's question involves formulating a nonlinear programming problem to find the optimal price for sandals that maximize total monthly profit for Native Customs. The decision variables in this context are the price per pair of sandals (P) and the monthly demand (D(P)). Given the cost of producing a pair of sandals ($18) and the price elasticity of demand provided by the function D(P) = 400 - 10P, the objective is to maximize the profit function, which can be formulated as Profit(P) = P × D(P) - Cost × D(P). As the price cannot exceed $35, the optimal price must be determined within the constraint 0 ≤ P ≤ 35. The solution to this problem will provide the optimal price that Native Customs should charge for a pair of sandals to maximize their monthly profit.