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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