Bakery Question

Question

a baker sells loaves of bread in two different sizes: small and large. the baker has 40kg of flour to work with. small loaves require 0.4kg of flour and large ones require 0.8kg of flour. additionally, the baker has 800g of yeast; each loaf of bread requires 10g . if the baker makes $1.20 from each large loaf and $0.5 from each small loaf, and he wants to maximize profits, how many loaves of each size should he make?

Answer 1

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