Need help with parts A,B, and C. Please show work Joanne sells silk-screened T-s

Question

Need help with parts A,B, and C. Please show work

Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one T-shirt is $3.50. Her total cost to produce 70 T-shirts is $295, and she sells them for $8 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 $600? a. The linear cost function is C(x)=

Explanation / Answer

a) Total Variable cost = Marginal cost x Quantity = 3.50Q

If Q = 70 then TVC = 70 x 3.50 = 245

TC = 295

Implies, TFC = TC - TVC = 295 - 245 = 50

TC = 50 + 3.50Q

b) Break even is where TR - TC = 0

TR = TC

Price x Quantity = 50 + 3.5Q

8Q = 50 + 3.5Q

8Q - 3.5Q = 50

4.5Q = 50

Q = 500/45 = 100/9 = 11.1 or 11 shirts

c) Profit = TR - TC

600 = 8Q - 50 - 3.5Q

650 = 4.5Q

Q = 650/4.5 = 144.44 T-shirts

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