Question

A company distributes college logo sweatshirts and sells them for $45 each. The total cost function is linear, and the total cost for 80 sweatshirts is $3912, whereas the total cost for 240 sweatshirts is $6952.
a. what is the equation for the revenue function?
b. What is the equation for the total cost function?
c. Find the break even quantity.

Answer 1

(a) The total revenue function is TR = 45Q

(b) The total cost equation function TC = 2392 + 19Q

(c) Equilibrium quantity is 92

The total cost function can be written,

TC = a + b Q,

Where TC is the total cost ,a fixed cost ,

b is the variable cost per unit and

Q the quantity produced.

Revenue function can be given,

TR = P * Q,

Where TR is total revenue,

P is the price per unit and

Q quantity sold

since Q is $45

TR = 45 Q

When TC = $3912,

3912 = a + 80b              (Equation - 1)

When TC = $6952

6952 = a + 240b            (Equation - 2)

Solving simultaneously,

We subtract equation 1 from 2

6952 = a + 240b

3912 = a + 80b      

We can subtract the equation - 1 and  2 ,

3040 = 160b

3040 / 160 = b

b = $19

We substitute for b in any of the equations

3912 = a + 80b      

3912 = a + 80*19

3912 = a + 1520

3912 - 1520 = a

a = 2392

Hence the total cost equation is

TC = a + b Q,

TC = 2392 + 19Q

At equilibrium TC =TR

45 Q = 2392 + 19Q

45Q - 19Q = 2392

26Q = 2392

Q = 2392 / 26

Q = 92

Therefore,

(a) The total revenue function is TR = 45Q

(b) The total cost equation function TC = 2392 + 19Q

(c) Equilibrium quantity is 92

To learn more about Equilibrium visit :

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