Question 637391
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Let *[tex \LARGE x] represent the number of basic chairs manufactured in a given day.  Let *[tex \LARGE y] represent the number of deluxe chairs made.


The profit function is then *[tex \LARGE P(x,y)\ =\ 12x\ +\ 8y]


The constraints are:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ y\ \leq\ 150]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ \leq\ 100]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ \leq\ 75]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ \geq\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ \geq\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x,\,y\,\in\ \mathbb{Z}]


The last constraint is that the values of the variables must be integers since you have to sell whole chairs; any possible fractional part of a chair could not be part of the solution.


Graph each of the constraint inequalities on one set of axes.  The pentagonal (5-sided) area where the solution sets ALL overlap is the area of feasibility.


The optimum point is one of the vertices of the feasibility polygon.  Test the coordinates of each of the vertices in the Objective (Profit) function.  The set of coordinates that gives you the largest profit value is the optimum solution.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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