You manage an ice cream factory that makes two flavors: Creamy Vanilla and Conti

Question

You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. You have in stock 550 eggs and 900 cups of cream. You make a profit of $3 on each quart of Creamy Vanilla and $2 on each quart of Continental Mocha. How many quarts of each flavor should you make in order to earn the largest profit? HINT [See Example 2.] (If an answer does not exist, enter DNE.) Creamy Vanilla quarts Continental Mocha quarts Ruff, Inc. makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 222 grams of protein and at least 152 grams of fat. If chicken costs 11 per ounce and grain costs 1 per ounce, how many ounces of each should Ruff use in each bag of dog food in order to minimize cost? HINT [See Example 4.] (If an answer does not exist, enter DNE.) grain oz chicken oz

Explanation / Answer

1.

Let us suppose we make X creamy vanilla and Y mocha

constraing of egg

2X+Y<=550

constraint of cream 3X+3Y<=900

X+Y<=300

profit earned = 3X+2Y

we have to maximise 3X+2Y

after drawing the constraint equation we get corner points as (0,300) and (225,0) and (250,50)

values of profit for each case= 600 , 675 , 850

so for maximum profit make 250 creamy vanilla and 50 mochas

2

similar to above answr

equations are

10X+2Y>=222

5X+2Y>=152

cost 11X+Y

minimise cost by using the same method

the point for which cost iis minimum should be adopted

I hope you got my point

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