Question

H-E-B buys cases of almonds and walnuts. Almonds are packaged 15 bags per case and walnuts are packaged 17 bags per case. H-E-B orders no more than 200 bags of almonds and walnuts at a time. H-E-B pays $24 per case of almonds and $27 per case of walnuts, but will not order more than $300 total at any one time. H-E-B makes a profit of $8 per case on almonds and $9 per case on walnuts.a)Express the constraints in terms of x and y, where x is case of almonds and y is case of walnuts.b)Graph and find the feasible region, identify the vertices.c)Find the Objective Functiond)Using the objective function and the vertices of the feasible region, determine how many cases of almonds and how many cases of walnuts H-E-B should sell to maximize its profit.

Answer 1

x is case of almonds and y is case of walnuts.

Almonds are packaged 15 bags per case and walnuts are packaged 17 bags per case.

H-E-B orders no more than 200 bags of almonds and walnuts at a time.

So,

x + y < 200

where x and y refers to the number of bags

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H-E-B pays $24 per case of almonds and $27 per case of walnuts, but will not order more than $300 total at any one time.

But keep in mind that : Almonds are packaged 15 bags per case and walnuts are packaged 17 bags per case.

So,

24 * (x/15) + 27 * (y/17) < 300

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The constraints are:

x + y < 200

(24/15) x + (27/17) y < 300

So, the graph of the previous constraints is as following :