In this lesson, you will set up a system of inequalities to fit a particular situation.  Careful reading of the problem  and something to write on will be useful as you set up the inequalities.

To get started, look at this Example.

Example

A bakery sells fresh brownies and cupcakes on Saturday and Sunday afternoons.  The bakery charges $2 for each brownie and $3 for each cupcake.  The bakery can produce no more than 65 items each day, but would like to make at least $150 each day.

Think about the combinations of brownies and cupcakes below.  Use the Online Calculator or a graphing calculator to help you determine which combination(s) fit the bakery’s requirements.

Combination A
30 brownies and 40 cupcakes

Combination B
28 brownies and 18 cupcakes

Combination C
25 brownies and 35 cupcakes

• Does Combination A fit the bakery’s requirements?  Interactive button. Assistance may be required. ____________ No.   Why or why not?  Interactive button. Assistance may be required. ____________ The total number of items exceeds the maximum amount of items the bakery can produce each day.
  



• Does Combination B fit the bakery’s requirements? Interactive button. Assistance may be required. ____________ No.
    Why or why not?  Interactive button. Assistance may be required. ____________ The total amount of money made does not meet the minimum amount the bakery would like to make each day.



• Does Combination C fit the bakery’s requirements?  Interactive button. Assistance may be required. ____________ Yes Why or why not?  Interactive button. Assistance may be required. ____________ The number of items produced and the amount of money made both fit within the bakery’s requirements.

Click on the blanks below to check your answers.

Let x represent the number of brownies sold each day and y represent the number of cupcakes sold each day. On your own piece of paper, write an inequality to describe how many items can be produced at the bakery each day. Did you write Interactive button. Assistance may be required. _____________ x + y ≤ 65 ?

Write an inequality to describe the amount of money the bakery would like to make each day. Did you write Interactive button. Assistance may be required. _____________ 2x + 3y ≥ 150 ?

The bakery changes the price of the brownies to $2.50 each and cupcakes to $3.75 each.  They increase their production level to no more than 80 items and want to make at least $225.  Let x represent the number of brownies sold each day and y represent the number of cupcakes sold each day.

Write a system of inequalities for this new situation. Did you write Interactive button. Assistance may be required. _____________ x + y ≤ 80 and Interactive button. Assistance may be required. _____________ 2.5x + 3.75y ≥ 225 ?