Use the simplex method to solve the following

Question

A baker has 10 cups of flour, 12 cups of sugar, and 24 eggs. A loaf of raisin bread requires a cup of flour,
2 cups of sugar, and 4 eggs, while a raisin cake requires a cup of flour, a cup of sugar and 2 eggs. If raisin
bread sells for $4/loaf and the cake sells for $5/each, how much of each should be baked so that the
bakers ' revenue is maximized?

Answer 1

 

X is the loaves of Raisin bread

Y is the loaves of  raisin cake

 

flour:  X + Y = 10

sugar:  2X +Y = 12

eggs:  4X + 2Y = 24 --> 2x + y = 12

 

 

 

X+Y = 10 --> y = 10 - x = -x + 10

2x + y = 12 ---> y = -2x + 12 

 

The lines meet at -x + 10 = -2x + 12

                           -x + 10 + 2x - 12 = 0

                            x - 2 = 0

                            x = 2 ---> y = (-2)(2) + 12 = -4 + 12 = 8

 

The lines meet at (2,8)

 

 

The feasibility reason is x>0, y>0

The edge points are (0,10), <--- the y intercept of y =-x+10

                             (2,8),

                             (6,0) <-- the x intercept of y = -2x + 12

 

 

bounded above by y = -x + 10 and to the right by y = -2x + 12

 

The revenue function is C(x,y) = 4x + 5y

 

C(0,10) = 4(0) + 5(10) = 0 + 50 = 50

 

C(2,8) = 4(2) + 5(8) = 8 + 40 = 48

 

C(6,0) = 4(6) + 5(0) = 24