ABC company cost function for the next four months is C=500000+5q required :
a The break -even dollar volume of sales if the selling price is birr 6 per unit.
b what would be the compans cosu if it decided to shut down operations for the next four months ?
6 q = 5 q + 500,000
so 500,000
if q = 0 then c = 500,000
3000000
a) To find the break-even dollar volume of sales, we need to set the cost function equal to the revenue function and solve for the sales quantity (q).
Given:
Cost function (C) = 500,000 + 5q
Selling price per unit = 6
Revenue function = Selling price per unit * Quantity (q) = 6q
At the break-even point, the revenue equals the cost:
6q = 500,000 + 5q
Rearranging the equation:
6q - 5q = 500,000
q = 500,000
To find the break-even dollar volume of sales, we multiply the break-even quantity (q) by the selling price per unit:
Break-even dollar volume of sales = q * Selling price per unit = 500,000 * 6 = 3,000,000 birr
b) If the company decides to shut down operations for the next four months, there would be no production and no costs. Therefore, the company's cost would be zero.
To find the break-even dollar volume of sales, we need to set the total cost equal to the total revenue and solve for the quantity (q) of units sold. The total cost equation is given as C = 500000 + 5q.
a) Break-even dollar volume of sales:
Since the selling price is birr 6 per unit, the total revenue is simply the selling price (SP) multiplied by the quantity sold (q). Therefore, the total revenue equation is TR = SP * q.
To find the break-even point, we equate the total cost (C) to the total revenue (TR) and solve for q:
500000 + 5q = 6q
Simplifying the equation:
-q = 500000
q = -500000
The break-even point cannot be negative. Hence, it means that the company will not break even at a selling price of birr 6 per unit.
b) Company's cost if it decides to shut down operations for the next four months:
If the company decides to shut down operations, there will be no units sold (q = 0). Therefore, to find the cost, we substitute q = 0 into the cost function:
C = 500000 + 5(0)
C = 500000
The company's cost, if it decides to shut down operations for the next four months, will be birr 500,000.