Answer to Question #259161 in Linear Algebra for Anisha

Question

A department store has overhead costs of $250; 000 and a linear total cost function. The controller has set the

store's margin policy using the example of a $140 markup on an item retailing for $500. The controller has also

estimated that other variable costs on the same retail item selling for $500 are $15.

i. Find the revenue, cost, and prot functions using s for sale volume.

ii. Find the break-even dollar volume of sales.

iii. Draw the break-even chart.

iv. What will the net prot be if sales are $3; 000; 000 ?

Answer 1

i. The revenue function is: TR = 500s.

The total cost function is: TC = 25,000 + 375s.

The profit function is:

TP = TR - TC = 125s - 25,000.

ii. The break-even dollar volume of sales is:

$BEP = 25,000/(500 - 375) = 200$ units.

iii. The break-even chart is a graphical representation of costs at various levels of activity shown on the same chart as the variation of income (or sales, revenue) with the same variation in activity.

iv. If sales are $3,000,000, then the net profit is:

$TP = 125×(3,000,000/500) - 25,000 = 350.$