Question

A software company incurs a cost of $50 per license sold plus $5,000 in fixed costs. How many licenses should you sell to minimize total costs?

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Timmothy

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68 Answers

To minimize the total costs, you should find the number of licenses you need to sell to cover the fixed costs and the variable costs per license. In this case, the cost function can be represented as follows:
Total Cost (C) = Fixed Costs + (Variable Cost per License) * (Number of Licenses Sold)
Fixed Costs = $5,000
Variable Cost per License = $50
Let's denote the number of licenses to be sold as "x." We want to minimize the total cost, so we need to find the value of "x" that minimizes the total cost.
The total cost function is:
C(x) = $5,000 + $50x
Now, to minimize the total cost, set up a cost equation where the total cost equals the revenue, which is the product of the number of licenses sold and the selling price (assuming that you're selling each license for a certain price "p"):
C(x) = p * x
Now, you need to find the price "p" that covers both the fixed and variable costs. Substituting the values:
$5,000 + $50x = p * x
Now, you want to isolate "x" to find the number of licenses to sell. Start by subtracting $5,000 from both sides:
$50x = p * x - $5,000
Now, factor out "x" from the right side:
$50x = x(p - $5,000)
Now, divide both sides by "x":
$50 = p - $5,000
Add $5,000 to both sides:
$5,050 = p
So, you should sell each license for at least $5,050 to cover both the fixed and variable costs. The number of licenses you need to sell to minimize the total costs is not influenced by the selling price; it remains "x."

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