For a given week, Jose's Coffee House has available 1584 ounces of A grade coffee and 1440 ounces of B grade coffee. These are blended into 1-pound packages as follows: an economy blend that contains 3 ounces of A grade coffee and 6 ounces of B grade coffee, and a superior blend that contains 11 ounces of A grade coffee and 4 ounces of B grade coffee. (The remainder of each blend is made of filler ingredients.) There is a $2 profit on each economy blend package sold and a $4 profit on each superior blend package sold. Assuming that the coffee house is able to sell as many blends as it makes, how many packages of each blend should it make to maximize its profit for the week? Note that the ALEKS graphing calculator can be used to make computations easier. Economy blend: package(s)

For a given week, Jose's Coffee House has available 1584 ounces of A grade coffee and 1440 ounces of B grade coffee. These are blended into 1-pound packages as follows: an economy blend that contains 3 ounces of A grade coffee and 6 ounces of B grade coffee, and a superior blend that contains 11 ounces of A grade coffee and 4 ounces of B grade coffee. (The remainder of each blend is made of filler ingredients.) There is a $2 profit on each economy blend package sold and a $4 profit on each superior blend package sold. Assuming that the coffee house is able to sell as many blends as it makes, how many packages of each blend should it make to maximize its profit for the week? Note that the ALEKS graphing calculator can be used to make computations easier. Economy blend: package(s)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Profit Maximization Problem for Jose's Coffee House

For a given week, Jose's Coffee House has available 1584 ounces of A grade coffee and 1440 ounces of B grade coffee. These are blended into 1-pound packages as follows:

- **Economy blend**: Contains 3 ounces of A grade coffee and 6 ounces of B grade coffee.
- **Superior blend**: Contains 11 ounces of A grade coffee and 4 ounces of B grade coffee.

(The remainder of each blend is made of filler ingredients.)

There is a $2 profit on each economy blend package sold and a $4 profit on each superior blend package sold. Assuming that the coffee house is able to sell as many blends as it makes, how many packages of each blend should it make to maximize its profit for the week?

Note that the [ALEKS graphing calculator](#) can be used to make computations easier.

#### Diagram Explanation

Below is a table to fill in the number of packages needed for each blend to maximize profit:

- Economy blend: [ ] package(s)
- Superior blend: [ ] package(s)

Expert Solution

Step 1: given data

Let x be the number of packages of Economy blend and y be the number of packages of Superior blend.

From the given data, make a table.

	A grade coffee	B grade coffee	Profit
x	3	6	$2
y	11	4	$4
Total	1584	1440

Our system is,

$M a x thin space thin space z equals 2 x plus 4 y$

Subject to

$3 x plus 11 y less or equal than 1584$

$6 x plus 4 y less or equal than 1440$

$x comma y greater or equal than 0$

Step by step

Solved in 4 steps with 5 images

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