Sales_Systems_of_Equations.doc

Sales: Systems of Equations

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A family owned bakery ran by the Merry Bakers is wanting to expand their production of breads to a local distributor, Fantastic Breads. They need your help in determining their breakeven point for production and the profit they would make by selling their bread to the distributor.

The Merry Bakers most popular breads are Pumpkin and Swedish Soda. They have 24 cups of flour and 26 teaspoons of baking powder on hand. Click on each box to put in your answers.

1. List three different combinations of Pumpkin and Swedish Soda Breads that the Merry Bakers can make using their ingredients.

2. Create an equation for the amount of flour the Merry Bakers will use for both the Pumpkin Bread and the Swedish Soda Bread. Remember, there are 24 cups of flour according to the directions. Hint: Let P = pumpkin bread and W = Swedish soda bread.

3. Create an equation for the amount of baking powder the Merry Bakers will use for both the Pumpkin Bread and the Swedish Soda Bread. Remember: there are 26 teaspoons of baking powder according to the directions. Hint: Let P = pumpkin bread and W = Swedish soda bread.

4. Use two methods of solving systems of equations to solve for the equations you created above.

A. Method 1 (substitution)

B. Method 2 (elimination)

C. Method 3 (graphing)

5. Based on your work above, what is the break-even point for the Merry Bakers with the ingredients they have on hand? Basically, how many Pumpkin and Swedish Soda Breads can they make to maximize their use of ingredients.

6. Why would it be beneficial to use two different methods when solving systems of equations?

7. The Merry Bakers would like to create a new type of bread and sell it to their distributor, Fantastic Breads. To make a new type of bread the Merry Bakers have an initial fee of $2250 for supplies then an additional $500 for every 50 loaves of bread made. They can sell the bread to Fantastic breads for $25 a loaf.

Below is the graph of C(n) and R(n) on the same axes.

a. Determine the cost of production function C(n) where n is the number of loaves of breads made.

b. Determine the revenue function R(n).

c. How many loaves of bread need to be produced in order to “break even”?

d. Profit can be calculated by P(n) = R(n) – C(n). Calculate the profit made on producing 400 loaves of bread.

e. Profit can be calculated by P(n) = R(n) – C(n). Calculate the profit made on producing 750 loaves of bread.

Please turn into the Sales Systems of Equations Dropbox to be graded.