Native Customs Sells Two Popular Styles of Hand-Sewn Footwear: a Sandal

question 11

Essay

Native Customs sells two popular styles of hand-sewn footwear: a sandal and a moccasin. The cost to make a pair of sandals is $18, and the cost to make a pair of moccasins is $24. The demand for these two items is sensitive to the price, and historical data indicate that the monthly demands are given by S = 400 -10P₁ and M = 450 - 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 $60 and $75 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.

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Definitions:

Monopolistically Competitive

In a monopolistically competitive market, firms sell products that are not perfect substitutes for each other, leading to some degree of market power but with free entry and exit in the long run.

Positive Profit

A financial gain that occurs when the revenues from business activities exceed the expenses, costs, and taxes needed to sustain the operation.

Tangent

A straight line that touches a curve at a single point without crossing it at that point.

Long-run Equilibrium

A state in a market where all firms are making normal profits, with no incentives for entry or exit, and all factors of production are variable.