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

question 28

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:

Oral

Pertaining to the mouth, including the administration of medicine or other substances through the mouth.

Rectal

Pertaining to, situated at, or involving the rectum, which is the final section of the large intestine.

Celsius

A scale for measuring temperature in which water freezes at 0 degrees and boils at 100 degrees under standard conditions.

Fahrenheit

A temperature scale where water freezes at 32 degrees and boils at 212 degrees under standard atmospheric conditions.