company’s cost function for the next four months is
C = 500,000 + 5Q
A. Find the BE dollar volume of sales if the selling price is br. 6 / unit
B. What would be the company’s cost if it decides to shut down operations for the next four
months
C. If, because of strike, the most the company can produce is br. 100,000 units, should it
shut down? Why or why no
A. To find the break-even (BE) volume of sales, we need to compare the selling price per unit and the cost per unit. Given that the selling price is br. 6 per unit and the cost function is C = 500,000 + 5Q, we can set the two equal to each other and solve for Q:
Selling price per unit = Cost per unit
br. 6 = 500,000 + 5Q
To isolate Q, subtract 500,000 from both sides:
5Q = br. 6 - 500,000
Divide both sides by 5:
Q = (br. 6 - 500,000) / 5
Now substitute the selling price into the equation:
Q = (6 - 500,000) / 5
Simplify the expression:
Q = -499,994 / 5
Q = -99,998.8
Since you cannot sell a negative quantity, the break-even volume of sales would be 0 units.
B. If the company decides to shut down operations for the next four months, its costs would be zero. This is because the cost function C = 500,000 + 5Q would not be applicable if no production or sales occur. Therefore, the cost would be 0 if the company decides to shut down.
C. If the company can only produce a maximum of 100,000 units due to a strike, we need to compare the cost of production with the potential revenue from sales. To determine if the company should shut down, we need to calculate the cost of producing 100,000 units.
Given that the cost function is C = 500,000 + 5Q, we can substitute Q = 100,000 into the equation to find the cost:
C = 500,000 + 5(100,000)
C = 500,000 + 500,000
C = br. 1,000,000
Therefore, the cost to produce 100,000 units is br. 1,000,000.
To decide whether the company should shut down, we compare the cost of production to the potential revenue from selling 100,000 units.
If the revenue from selling 100,000 units is greater than br. 1,000,000, it would be profitable for the company to continue production, even with reduced capacity due to the strike. However, if the revenue is less than br. 1,000,000, it may be more cost-effective for the company to shut down operations.
It's important to consider other factors such as fixed costs, market demand, and potential future implications before making a final decision.