Question

Willy Wonka has 2 candies, Wonka bars and Everlasting Gobstoppers. Both have both natural sugar and sucrose in them. Each Wonka Bar has 4 grams of natural sugar and 1 gram of sucrose. Each Everlasting Gobstopper has 2 grams of natural sugar and 3 grams of sucrose. Mr. Wonka has 60 grams of natural sugar and 75 grams of sucrose. If each Everlasting Gobstopper has a profit of $1.3 and each Wonka Bar has a profit of $3.2, how many of each candy would give him the maximum profit?

Answer 1

Answer:

Wonka bars=3 and  Everlasting Gobstoppers=24

Step-by-step explanation:

let the wonka bars be X

and everlasting gobstoppers be Y

the objective is to

maximize 1.3x+3.2y=P

subject to constraints

natural sugar

4x+2y=60------1

sucrose

x+3y=75---------2

x>0, y>0

solving 1 and 2 simultaneously we have

4x+2y=60----1

x+3y=75------2

multiply equation 2 by 4 and equation 1 by 1 to eliminate x we have

 4x+2y=60

 4x+12y=300

-0-10y=-240

10y=240

y=240/10

y=24

put y=24 in equation 2 we have'

x+3y=75

x+3(24)=75

x+72=75

x=75-72

x=3

put x=3 and y=24 in the objective function we have

maximize 1.3x+3.2y=P

1.3(3)+3.2(24)=P

3.9+76.8=P

80.7=P

P=$80.9