A product may be made using machine I or machine II. The manufacturer estimates that the monthly fixed costs of using machine I are $18,000, whereas the monthly fixed costs of using machine II are $15,000. The variable costs of manufacturing 1 unit of the product using machine I and machine II are $10 and $20, respectively. The products sell for $50 each. What is the maximum profit if the projected sales are 650 units?
a. $8,150
b. $8,100
c. $8,000
d. $8,200
e. $8,050
Can someone please explain this?
Thank you.
Answer is c 8,000 machine I
To find the maximum profit, first, we need to calculate the profit for each machine and compare them to determine which one will result in a higher profit.
For machine I:
Fixed costs (per month) = $18,000
Variable costs (per unit) = $10
Selling price (per unit) = $50
To calculate the profit, we need to subtract the total costs (fixed costs + variable costs) from the total revenue (selling price * number of units sold). Let's calculate it:
Total revenue = Selling price * number of units sold
Total revenue = $50 * 650 = $32,500
Total costs = Fixed costs + Variable costs * number of units sold
Total costs = $18,000 + $10 * 650 = $18,000 + $6,500 = $24,500
Profit = Total revenue - Total costs
Profit = $32,500 - $24,500 = $8,000
Now let's calculate the profit for machine II:
Fixed costs (per month) = $15,000
Variable costs (per unit) = $20
Total revenue = Selling price * number of units sold
Total revenue = $50 * 650 = $32,500
Total costs = Fixed costs + Variable costs * number of units sold
Total costs = $15,000 + $20 * 650 = $15,000 + $13,000 = $28,000
Profit = Total revenue - Total costs
Profit = $32,500 - $28,000 = $4,500
Comparing the profits of both machines, we can see that machine I will result in a higher profit.
Therefore, the maximum profit if the projected sales are 650 units is $8,000.
Hence, the correct answer is c. $8,000.
To determine the maximum profit, we need to calculate the profit for each machine and then compare the results.
For machine I:
Fixed Costs = $18,000
Variable Costs per unit = $10
Selling Price per unit = $50
Projected Sales = 650 units
Total Variable Costs for machine I = Variable Costs per unit * Projected Sales = $10 * 650 = $6,5000
Total Costs for machine I = Fixed Costs + Total Variable Costs = $18,000 + $6,500 = $24,500
Total Revenue for machine I = Selling Price per unit * Projected Sales = $50 * 650 = $32,500
Profit for machine I = Total Revenue - Total Costs = $32,500 - $24,500 = $8,000
For machine II:
Fixed Costs = $15,000
Variable Costs per unit = $20
Selling Price per unit = $50
Projected Sales = 650 units
Total Variable Costs for machine II = Variable Costs per unit * Projected Sales = $20 * 650 = $13,000
Total Costs for machine II = Fixed Costs + Total Variable Costs = $15,000 + $13,000 = $28,000
Total Revenue for machine II = Selling Price per unit * Projected Sales = $50 * 650 = $32,500
Profit for machine II = Total Revenue - Total Costs = $32,500 - $28,000 = $4,500
Since the question asks for the maximum profit, we choose the higher profit between machine I and machine II:
Maximum Profit = $8,000 (Machine I Profit)
Therefore, the correct answer is c. $8,000.