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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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Chapter
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BuyFindarrow_forward

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Resource Allocation You manage an ice cream factory that makes three flavors: Creamy Vanilla, Continental Mocha, and Succulent Strawberry. Into each batch of Creamy Vanilla go 2 eggs, 1 cup of milk, and 2 cups of cream. Into each batch of Continental Mocha go 1 egg, 1 cup of milk, and 2 cups of cream, while into each batch of Succulent Strawberry go 1 egg, 2 cups of milk, and 1 cup of cream. You have in stock 350 eggs, 350 cups of milk, and 400 cups of cream. How many batches of each flavor should you make in order to use up all of your ingredients? [HINT: See Example 1.]

To determine

To calculate: The number of batches of each flavor to be produced to fulfill all the resources. The factory produces 3 flavors creamy vanilla, continental mocha, and succulent strawberry. Creamy vanilla requires 2 eggs, 1 cup of milk and 2 cups of cream, continental mocha requires 1 egg, 1 cup of milk and 2 cups of cream and succulent strawberry requires 1 egg, 2 cups of milk and 1 cup of cream. The total stock is 350 eggs, 350 cups of milk and 400 cups of cream.

Explanation

Given Information:

The total stock is 350 eggs, 350 cups of milk and 400 cups of cream.

Also, Creamy vanilla requires 2 eggs, 1 cup of milk and 2 cups of cream, continental mocha requires 1 egg, 1 cup of milk and 2 cups of cream and succulent strawberry requires 1 egg, 2 cups of milk and 1 cup of cream. The total stock is 350 eggs, 350 cups of milk and 400 cups of cream.

Formula Used:

Elimination method:

In this method, we first combine the equations in a way such that one of the variables gets eliminated. Then we substitute this obtained value in either of the equation to get the value of the other variable.

Calculation:

let the number of batches of each flavor produced be x,y,z respectively.

And the given data gives the number of eggs, a cup of milk and cups of cream to be added in each batch of each flavor.

From the given information we can arrange the data in a table.

Batch of creamy vanilla (x) Batch of continental mocha (y) Batch of succulent strawberry (z) Total availability
Eggs 2 1 1 350
Cups of milk 1 1 2 350
Cups of cream 2 2 1 400

From the table, the equations for all the ingredients can be set up:

Eggs: 2x+y+z=350 ……(1)

cups of milk: x+y+2z=350 ……(2)

cups of cream: 2x+2y+z=400 ……(3)

Apply the elimination method to find the solution of the given system of the equations:

Begin by subtracting the second equation from the first equation to eliminate y

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