Assume that each gallon of Deluxe Vanilla uses 2 quarts of milk, 2 quarts of cre
ID: 3121513 • Letter: A
Question
Assume that each gallon of Deluxe Vanilla uses 2 quarts of milk, 2 quarts of cream, and 2 ounces of vanilla; each gallon of Regular Vanilla uses 3 quarts of milk, 1 quart(s) of cream, and 1 ounces of vanilla; and each gallon of Deluxe Chocolate uses 3.5 quarts of milk, 0.5 quarts of cream, and 8 ounces of cacao. Assume also that the shop has on hand 150 gallons of milk, 74 gallons of cream, 16 pounds of vanilla, and 40 pounds of cacao. How many gallons of each type of ice cream should the shop make to use up all of these ingredients?
When you setup a system of linear equations to solve this problem, how many variables and how many equations should you have.?
Explanation / Answer
1ST PART
Given :
DELUXE VANILLA
2 quarts milk
2 quarts cream
2 ounces vanilla =0.0625
REGULAR VANILLA
3 quarts milk
1 quarts cream
1 ounces vanilla = .03125
DELUXE CHOCOLATE
3.5 quarts milk
.5 quarts cream
8 ounces Cacao = .25
SHOP has
150 gallons milk = 150*4 = 600 quarts
74 gallons cream = 74*4 = 296 quarts
16 pounds vanilla = 16*16 = 256 ounces = 8 quarts
40 pounds Cacao = 40*16 = 640 ounces = 20 quarts
Total =924
We know,
1 gallon = 4 quarts
1 gallon = 8.25 pounds (taking standard)
1 pounds = 16 ounces
total material need :
DELUXE VANILLA = 4.0625 quarts
REGULAR VANILLA = 4.03125 quarts
DELUXE CHOCOLATE = 4.25 quarts
2x + 2y + 0.0625z = 4.0625
3x + y + 0.03125z = 4.03125
3.5x + 0.5y + .25m = 4.25
--------------------------------------------------------
8.5x + 3.5y + 0.09375 z +.25m = 12.34375
unit milk used = 600/8.5 = 70.58
unit cream used = 296/3.5 = 84.57
unit vanilla used = 8/0.09375 = 85.33
unit cacao used = 20/.25 = 80
Therefore, 70 units of icecream are produced.
17.5 units of each Icecream is produced.
2ND PART :
4 variables are used : x , y , z , m
4 equations are used :
2x + 2y + 0.0625z = 4.0625
3x + y + 0.03125z = 4.03125
3.5x + 0.5y + .25m = 4.25
8.5x + 3.5y + 0.09375 z +.25m = 12.34375