Answer to Question #274850 in Calculus for sumu

Question

5. Suppose you plan to set up a firm to retail a certain product A. From a market survey, you estimate that the annual sales volume is 20,000 units at a selling price of $25 per unit. You can purchase product A from a manufacturer at a cost of $13 per unit. Total fixed cost, which includes rental, depreciation, etc. is estimated at $180,000 per annum.

(a) Calculate the break-even point in units, in dollars.

(b) Calculate the profit based on the expected sales volume.

Answer 1

Sales price of each unit is $25

Variable cost of each unit is $13

Fixed cost per annum = $180000

Let the number of units purchased as well as sold = x

So total revenue = $25x

And total cost = $ (180000+13x)

For break even point

Total revenue = Total cost

=> $25x = $(180000+13x)

=> 25x = (180000+13x

=> 25x - 13x = 180000

=> 12x = 180000

=> $=> x = \frac{180000}{12}=15000$

(a) The break-even point in units is 15000 units

The break-even point in dollars is $25*15000 = $375000

(b) The profit based on the expected sales volume

= $ [20000*(25 - 13)-180000]

= $ (20000*12 - 180000)

= $(240000 - 180000)

= $ 60000