A producer can produce a product at a variable cost per unit of $6. The producer

Question

A producer can produce a product at a variable cost per unit of $6. The producer can sell the product for $10 each. If the fixed cost is $90,000

a. How many units must the producer sell to break-even?

b. What is revenue at 20,000 units? What is total cost at 20,000 units?

c. How many units must the producer sell in order to earn a profit of $60,000?

d. If the producer believes price can be raised without reducing the quantity you found in part c, what should the new price be to earn a profit of $75,000?

Explanation / Answer

Fixed cost (FC) = 90000

Variable cost (VC) = $6 per unit

Revenue (R) = $10 per unit

a) Break even point in units = FC / (R - VC)

= 90000 / (10-6)

= 90000/4

= 22500 units

So the producer must sell 22500 units to break even.

b) If Quantity of output (Q) = 20000 units,

Revenue = Q x R = 20000 x $10 = $200000

Total cost = FC + (Q x VC) = 90000 + (20000 x 6) = $90000 + $120000 = $210000

c) profit (P) = $60000

P = Q(R-VC) - FC

=> 60000 = Q(10-6)-90000

=> 60000 = 4Q - 90000

=> 4Q = 60000+90000

=> 4Q = 150000

=> Q = 150000/4

=> Q = 37500

So in order to earn a profit of $60000 the producer must sell 37500 units

d) Quantity (Q) = 37500 units

Profit (P) = $75000

P = Q(R-VC) - FC

=> 75000 = 37500(R-6)-90000

=> 75000 = 37500R - 225000 - 90000

=> 75000 = 37500R - 315000

=> 37500R = 75000+315000

=> 37500R = 390000

=> R = 390000/37500

=> R = 10.4

So the new price should be $10.4 per unit.

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