Answer:
a. The maximum profit that can be achieved is <u>$300,000</u>.
b. The unit price at this point of optimal demand is <u>$90</u>.
Explanation:
From the question, we can obtain the following:
x = Maximum expected demand = 6,000 units
Price = 150 - 0.01 x = 150 - (0.01 * 6,000) = 150 - 60 = $90
Fixed cost per year = $50,000
Variable cost per unit = $40
Total variable cost = Variable cost per unit * Maximum expected demand = $40 * 6,000 = $240,000
Total cost = Fixed cost + Total variable cost = $50,000 + $240,000 = $290,000
Revenue = Price * Maximum expected demand = $90 * 6,000 = $540,000
Therefore, we have:
a. What is the maximum profit that can be achieved if the maximum expected demand is 6,000 units per year?
Profit = Revenue - Total cost = $540,000 - $240,000 = $300,000
Therefore, the maximum profit that can be achieved is <u>$300,000</u>.
b. What is the unit price at this point of optimal demand?
As already stated above, the following are given in the question:
x = Maximum expected demand = 6,000
Price = 150 - 0.01 x ........................... (1)
Substitute for x in equation (1), we have:
Price = 150 - (0.01 * 6,000) = 150 - 60 = $90
Therefore, the unit price at this point of optimal demand is <u>$90</u>.
