# ALGEBRA 2

An apple pie uses 4 cups of apples and 3 cups of flour. An apple cobbler uses 2 cups of apples and 3 cups of flour. You have 16 cups of apples an 15 cups of flour. When you sell these at the Farmers market you make \$3.00 profit per apple pie and \$2.00 profit per apple cobbler. Use linear programming to determine how many apple pies and how many apple cobblers you should make to maximize profit.

Use linear programming to determine how many apple pies and how many apple cobblers you should make to maximize profit.
Let x=The number of apple pies you make. Let y=The number of apple cobblers you make Write an inequality to show the constraint on the amount of apples you have. If anyone could help me I'd be so grateful. I been struggling with this for 2 days. I am not just looking for quick answers I want to learn. If you have any links that could help with constraints that would be amazing.

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1. surely your text has a section on linear programming, where it explains problems just like this one.

Assign variables
write the constraints
define the objective function

evaluate at all the vertices of the region.

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2. Let's take this step by step.
1. We can let x = number of apple pies you would make and y= the number of apple cobblers you make.

2. We can make an inequality showing the constraint of apples we need. So: 4x+2y<=16. Done!

3. Next ingredient we would use is flour, so let's make an inequality for the amount of flower we have: 3x+3y<=15. Just to help explain how we got it

4. We need 4 cups of apples for an apple pie and we need 2 cups of apples for an apple cobbler. Same applies with the flour, we ned 3 cups of flour and 3 cups of flour for both the apple pie and flour.

5. So, next we can graph the equations we wrote, so graph that and then write down what the feasible region is. (Should be three points).

6. Now, we can write the maximum profit equation, which would be 3x+2y. (Reason why is because \$3 per apple pie and \$2 per apple cobbler). For this you can solve it yourself and just plug into what we found when we graphed it.

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3. Consider a duck swimming under water to catch a fish. His path can be written by the function . There is a piece of seaweed on the y-axis. X is time in seconds related to when he hits the seaweed. Y is his distance in feet under the water. Find and label each ordered pair. Match each vocabulary term with each moment (terms may be repeated).

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4. 2a. root (-10,0)
2b. vertex (-3,-49)
2c. y-intercept (0,-40)
2d. root (4,0)

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