A couple of college students get the idea to open a snack stand at the regatta festival this summer. The students sell delicious soft pretzels. They pay the city $648 to set up their stand for the entire regatta. They also figure the cost for dough, coarse salt, and other things they need is $0.20 per pretzel. They sell each pretzel for $2.90. a. What is the cost and the income obtained from selling forty pretzels?

b. If the income from selling the pretzels was $261, how many pretzels did they sell?

c. How many pretzels must they sell to break even, according to the algebraic model?

Answer:

a) The cost of producing 40 pretzels is $656

The income for selling 40 pretzels is $116

b) They sold 90 pretzels

c) They must sell 240 pretzels to break-even

Step-by-step explanation:

Linear Models

A linear model is an equation that describes a relationship between two quantities that have a constant rate of change.

One of the most-used equations of linear models is the slope-intercept form, written as:

y = mx + b

Where m is the slope of the graph of the line and b is the y-intercept.

The total cost of producing soft pretzels is divided into two parts:

* A fixed cost of $648 to set up their stand for the entire regatta.

* A variable cost of $0.20 per each pretzel.

Thus, the cost function can be written as:

C(x)=648+0.20x

Where x is the number of pretzels produced.

The students sell each pretzel for $2.90. This means the income (revenue) function for selling x pretzels is:

R(x)=2.90x

a) The cost of producing x=40 pretzels is:

C(40)=648+0.20*40

C(40)=648+8

C(40)=656

The cost of producing 40 pretzels is $656

The income is:

R(40)=2.90*40=116

The income for selling 40 pretzels is $116

b) If the income from selling pretzels is R=$261, then:

2.90x=261

Solving for x:

x = 261/2.90

x = 90

They sold 90 pretzels

c) To break-even the total cost and the income must be equal:

2.90x=648+0.20x

Subtraction 0.20x:

2.70x=648

Dividing by 2.70:

x = 648/2.70

x = 240

They must sell 240 pretzels to break-even

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