Question

Total Cost Analysis The manager of a rival T-shirt stand found that her cost to produce 10 T-shirts is $105.98, while the cost to produce 40 T-shirts is $398.42. Assume the cost C) is a linear function of x, the number of T-shirts produced. Find the total cost of producing 100 T-shirts.(Round to 2 decimal places)

Answer 1

Total Cost of Production 100 T-shirts is $983.30

C(x) = FC + Vx

​​​​​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

Now, Cost of Producing 10 T-shirts is $105.98

So, C(10) = FC + V*10

$105.98 = FC + 10V

FC = $105.98 - $10V

And, Cost of Producing 40 T-shirts is $398.42

So, C(40) = FC + V*40

$398.42 = FC + 40V

FC = $398.42 - 40V

Now we have two equations for fixed cost (FC)

Equating both

$105.98 - 10V = $398.42 - 40V

40V - 10V = $398.42 - $105.98

30V = $292.44

V = $9.748

So, Variable Cost per unit is $9.748

Putting V in FC = $105.98 - 10V

FC = $105.98 - (10 * $9.748).7

FC = $105.98 - $97.48

FC = $8.50

So, Fixed Cost is $8.50

Therefore

C(x) = $8.50 + $9.748x

So, Total Cost of Producing 100 t-shirts i.e. C(100) is

C(100) = $8.50 + ($9.748 * 100)

C(100) = $8.50 + $974.80

C(100) = $983.30

So, Cost of Producing 100 t-shirts is $983.30

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