An ice cream producing company produces 2 mixes of ice cream everyday: REGULAR and EXTRA which use 2 ingredients A & B. Each liter of regular contains 2 grams of ingredient A and 1 gram of ingredient B, while each liter of Extra contains 1 gram of ingredient A and 2 grams of ingredient B. The profit of each liter of regular is Php8 and the profit of each liter of extra is Php10. If the company has 50 grams of ingredient A and 70 grams of ingredient B available each day, how may liters of each mixes of ice cream should be made each day to maximize the profit?
Answers
Answer
Use the two steps for solving a linear programming problem, given in the box on page to solve the problems in Exercises Food and clothing are shipped to survivors of a natural disaster. Each carton of food will feed 12 people, while each carton of clothing will help 5 people. Fach 20 -cubic- foot box of food weighs 50 pounds and each 10 -cubic-foot box of clothing weighs 20 pounds. The commercial carriers transporting food and clothing are bound by the following aconstraints: The total weight per carrier cannot exceed pounds. The total volume must be less than 8000 cubic feet. How many cartons of food and clothing should be sent with each plane shipment to maximize the number of people who can be helped?
Php 380 liters is used for each mixes of ice cream should be made each day to maximize the profit
Step-by-step explanation:
Each litre of regular contains 2 grams of ingredient A and 1 gram of ingredient B.
Each litre of Extra contains 1 gram of ingredients A and 2 gram of ingredient B
The company has 50 grams of ingredient A
The company has 70 grams of ingredient B
Therefore we can take the equation as,
2x + y = 50 it is taken as equation for ingredient A
x + 2y = 70 it is taken as equation for ingredient B
Solve both the equation,
Multiply by 2 in the equation 1
we get,
4x+2y=100
x+2y=70
3x = 30
x = 10
Sub x=10 in eq
x + 2y = 70
10 + 2y = 70
2y = 60
y= 30
x=10 , y = 30
The profit of each liter of regular is Php8 and the profit of each liter of extra is Php10
Therefore the equation is
W = 8x + 10y
Sub the value of x and y in above equation
W = 8(10) + 10(30)
W = 80 + 300
W = 380
As the result the maximum profit ice cream is Php 380
Final answer:
Php 380 liters is used for each mixes of ice cream should be made each day to maximize the profit
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