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Linear Programming Project

By: Matthew Talavera Period 1

What do we need to figure out?

We need to know how much of each type of cookie should be in each package to maximize the profit and to find out what is the maximum profit.

Problem #2

Solution!

Let's get started!

Between the three vertices, vertice (3,9) made the most profit with 309.

So the answer is:

There are 3 chocolate chip cookies and 9 peanut butter cookies in each combination package and maximun profit you will get from is 309 cents.

Let x be the chocolate chip cookies.

Let y be the peanut butter cookies.

Since there are at least 6 cookies in each package and at most 12 cookies in each package, x+y is greater than or equal to 6 and is less than or equal to 12.

There are at least 3 of each type of cookie in each package, so x is greater than or equal to 3 and y is greater than or equal to 3.

The cost of each chocolate chip cookie is 19 cents and the cost for each peanut butter cookie is 13.

The profit for the chocolate chip cookies is 44 - 19= 25.

The profit for the peanut butter cookies is 39 - 13=26.

The objective function for the maximun profit is P= 25x + 26y.

The cafeteria's best selling items are chocolate chip cookies and peanut butter cookies. They want to sell both types of cookies together in combination packages. The different-sized packages will contain between 6 and 12 cookies, inclusively. At least three of each type of cookie should be in each package. The cost of making a chocolate chip cookie is 19 cents and the selling price is 44 cents. The cost of making a peanut butter cookie is 13 cents and the selling price is 39 cents. How many of each type od cookie should be in each package to maximize the profit? What is the maximum profit?

Now let's graph!

Now that we got our equations for our problems, let's get to graphing!

The vertices of the feasible region are (3,3), (9,3), and (3,9).

Objective Function:

P= 25x + 26y

Vertices:

(3,3); 25(3)+26(3)=153

(9,3); 25(9)+26(3)=303

(3,9); 25(3)+26(9)=309

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