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:

SSR

Sum of Squared Residuals; it quantifies the variance in observed values that is not explained by the predictive model.

SSE

Stands for Sum of Squared Errors, a measure used in statistics to quantify the discrepancy between the data and an estimation model.

Standard Error

A measure of the dispersion or variability of a sample statistic, such as the mean, from the population mean, often used to indicate precision.

Standard Error

The standard deviation of the sampling distribution of a statistic, most commonly the mean, reflecting the variability of an estimate from sample to sample.