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You manage an ice cream factory that makes two flavors: Vanilla and Mocha. Each quart of Vanilla requires 2 eggs and 3 cupsof cream. Each quart of Mocha requires 1 egg and 4 cups of cream. You have in stock 500 eggs and 1200 cups of cream. You make a profitof $3 on each quart of Vanilla and $5 on each quart of Mocha.a) How many quarts of each flavor should you make in order to earn the largest profit?b) Are there any leftover resources? Be specific.

Question

You manage an ice cream factory that makes two flavors: Vanilla and Mocha. Each quart of Vanilla requires 2 eggs and 3 cups
of cream. Each quart of Mocha requires 1 egg and 4 cups of cream. You have in stock 500 eggs and 1200 cups of cream. You make a profit
of $3 on each quart of Vanilla and $5 on each quart of Mocha.
a) How many quarts of each flavor should you make in order to earn the largest profit?
b) Are there any leftover resources? Be specific.

check_circleAnswer
Step 1

(a)

Let,

x = number of quarts of vanilla

y = number of quarts of Mocha

Now, as each quart of vanilla requires 2 eggs and 3cups of cream and each quart of Mocha requires 1 egg and 4 cups of cream, also it is given that there are 500 eggs 1200 cups of cream in stock, therefore we will have the following inequalities:

2к+ y<500
Зх +4y<1200
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2к+ y<500 Зх +4y<1200

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Step 2

Now, also there is profit of $3 on each quart of vanilla and $5 on each quart of Mocha, therefore, the maximization equation will be:

P 3x+5y
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P 3x+5y

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Step 3

So, here is the obtained Linear...

Maximize P 3x +5y
Subject to 2x y< 500
3x4y 1200
x20
y20
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Image Transcriptionclose

Maximize P 3x +5y Subject to 2x y< 500 3x4y 1200 x20 y20

fullscreen

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Algebra

Linear Programming

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