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Joanne sells​ silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one​ T-shirt is $ 5.50 . Her total cost to produce 70 ​T-shirts is $ 465 comma and she sells them for ​$9 each. a. Find the linear cost function for​ Joanne's T-shirt production. b. How many​ T-shirts must she produce and sell in order to break​ even? c. How many​ T-shirts must she produce and sell to make a profit of ​$700​?

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parodilucas

Answer:

Hey there!!

1) C(x) = 80 + 5.50x

2) 22.86 ≅ 23

3) 222.86 ≅ 223

Explanation:

1) C(x) = FC + V(x)

  465 = FC + 5.50 * 70

   FC = 465 - 385

   FC = 80

C is Total Cost

FC is Fixed Cost

V is Unit Variable Cost

We know that the variable cost is 5.50 per unit and that total cost for producing 70 T-shirts is $465.

By replacing in the formula and clearing, we can find out the value of the fixed cost of production and complete the total cost function.

2) First, we calculate the unit margin contribution

c = P - V

c = 9 - 5.50

c = 3.50

c is Unit Margin Contribution

P is Price

V is Unit Variable Cost

then we calculate break-even point

[tex]X= \frac{TFC}{c}\\\\X= \frac{80}{3.5} = 22.86[/tex]

TFC is Total Fixed Cost  

c is Unit Revenue

3) using the break-even point, we can calculate

[tex]X= \frac{TFC}{c}\\\\X= \frac{80+700}{3.5} = 222.86[/tex]