Question

Bus Econ 1.2.35 Question Help Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one T-shirt is $4.50. Her total cost to produce 50 T-shirts is $285, 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 $600? a. The linear cost function is C(x) = 4.50x + 80 b. Joanne must produce and sell 14 Tahits in order to break even c. Joanne must produce and set T-shirts to make a profit of $800. Enter your answer in the answer box and then click Check Answer All parts showing

Answer 1

Answer

a)

Linear Cost Function

C(x) = Vx + FC

​​​​​Where C(x) is the Total cost of producing x number of units

FC is the Fixed Cost

V is the Variable Cost per unit and X is the number of units produced

So, Vx is the Variable Cost of producing x number of units

Variable Cost per unit = $4.50 (given) i.e marginal cost of producing one unit

Now,

Total cost of producing 50 T-shirts = $285 (given)

So,

C(50) = FC + V(50)

$285 = FC + ($4.50 * 50)

$285 = FC + $225

FC = $60

Fixed Cost is $60

So, Linear Cost Function is

C(x) = 4.50x + 60

b)

Selling Price per unit = $9 (given)

So,

Revenue Function

R(x) = 9x

At break even point there is no profit or loss.

So,

R(x) - C(x) = 0

9x - (4.50x + 60) = 0

9x - 4.50x - 60 = 0

4.50x = 60

x = 60 / 4.50

x = 13.3333333

x = 14 units (rounded up because units can't be in points)

So, Joanne must produce and sell 14 T-shirts in order to break even

c)

Profit i.e P(x) = 600

P(x) = R(x) - C(x)

So,

600 = 9x - (4.50x + 60)

600 = 9x - 4.50x - 60

600 + 60 = 4.50x

660 = 4.50x

x = 660 / 4.50

x = 146.6666

x = 147 units (rounded up because units can't be in points)

So, Joanne must produce and sell 147 T-shirts to make a profit of $600.

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