MATH SOLVE

4 months ago

Q:
# Brew Ha Ha Coffee produces two types of coffee blends: Morning,x,and House,y. The Morning blend has 9oz of a Guatemalan coffee and 7oz of Brazilian coffee. The company makes $2 in profit from each bag of Morning Blend sold and $2.50 in profit from each bag of House Blend sold. The company has 400oz of both the Guatemalan and Brazilian coffees available.This set of inequalities represent the constraints in this situation.9x+6y<4007x+10y<400X>0Y>0The company wants to maximize its profits by using the objective function P = 2x + 2.5yWhat is the maximum profit.880160106

Accepted Solution

A:

Answer:Fourth optionStep-by-step explanation:When graphing the given inequalities you will get a region like the one shown in the attached image. This region is delimited by 4 straight
[tex]x = 0\\\\y = 0\\\\9x + 6y = 400\\\\7x + 10y = 400[/tex]The points indicated at the ends of the region are the maximum possible values of x and y.
We must test these points in the objective function [tex]P = 2x + 2.5y[/tex] and see which point maximizes the value of P.
Remember that the boundaries of the region are not included.
We can prove the point x = 0 and y = 39 because (0,4) is not included in the region.
[tex]P = 2(0) + 2.5(39) = 97.5[/tex]Now we test the point x = 33 and y = 16
[tex]P = 2(33) + 2.5(16) = 106[/tex]Now we test the point x = 44 and y = 0
[tex]P = 2(44) + 2.5(0) = 88[/tex]Finally the optimal value is:
x = 33 oz
y = 16 oz
With a gain of $106