(6 points) A baker sells loaves of bread in two different sizes: small loaves and large loaves. The baker has 40 kilograms of flour to work with. Small loaves require 0.4 kilograms of flour and large loaves require 0.8 kilograms of flour. Additionally, the baker has 800 grams of yeast. Each loaf of bread requires 10 grams of yeast. If the baker makes $1.20 profit from each large loaf and $0.50 profit from each small loaf, and he wants to maximize his profits, how many loaves of each size should he make?
Answers
Answer:
First arrange the information in a matrix. Let x represent the number of small loaves and y be the number of large loaves made.
flour yeast revenue
small x 0.4 10 0.50
large y 0.8 10 1.20
max 40 800
Write the objective function
z = 0.5x + 1.2y
Write the constraint equations and objective function
0.4x + 0.8y ≤ 40
10x + 10y ≤ 800
x, y ≥ 0, he cannot make negative quantity of a product
Graph the constraint equations and determine the feasible region.
There are four corner points. (0, 0), (80, 0), (0, 50) and (60, 20) the intersection of the two lines
Test the corner points in the objective function. The one that give the biggest value is the answer.
(0, 0) z = 0.5(0) + 1.2(0) = 0
(80, 0) z = 0.5(80) + 1.2(0) = 40
(0, 50) z = 0.5(0) + 1.2(50) = 60
(60, 20) z = 0.5(60) + 1.2(20) = 54
The baker should make 0 small loaves of bread and 20 large loaves of bread for a profit of $60
Step-by-step explanation:
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