Question

Brew Ha Ha & Tea Co. produces two types of coffee blends: Moring (x) and (y). The Morning Blend has 9 oz of Guatemalan coffee and 7 oz of Brazilian coffee, and the house blend has 6 oz of Guatemalan coffee and 10oz of Brazilian coffee. The company makes $2 in profit from each bag of the morning blend sold and $2.50 in profit from each bag of house blend sold. The company has 400 oz of both the Guatemalan and Brazilian coffees available. This set of inequalities represents the constraints in this situation. 9x + 6y< 400 7x + 10y<400 x > 0 y > 0 The company wants to maximize their profits using the objective function P = 2x + 2.5y What is the maximum profit? there is a chart for vertex and objective function

Answer 1

From the graph of the constraints, the corner points are: (0, 0), (0, 40), (33.33, 16.67), (44.44, 0)

For the corner points the profits are:
For (0, 0): P = 2(0) + 2.5(0) = 0
For (0, 40): P = 2(0) + 2.5(40) = 0 + 100 = 100
For (33.33, 16.67): P = 2(33.33) + 2.5(16.67) = 66.66 + 41.68 = 108.34
For (44.44, 0): P = 2(44.44) + 2.5(0) = 88.88

Therefore, the maximum profit is $108.34