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:

Returns

In a financial context, the profit or loss derived from an investment over a specified period of time, often expressed as a percentage of the investment's initial cost.

Ideas and Deeds

Refers to the conceptual and action-oriented aspects of initiatives or tasks, emphasizing the importance of both innovative thinking and practical implementation in achieving goals.

Fear and Force

Applies to methods of control or influence based on inducing fear or the application of coercion, often seen as negative leadership or management tactics.

Performance Standards

The expected levels of performance and achievements for a task, role, or activity within an organization.