How to Calculate Profit in a Business Venture

What is the minimum number of thing-a-ma-bobs that the company must produce and sell to make a profit?

With a start-up cost of $39,305, a production cost of $2.40 per thing-a-ma-bob, and a selling price of $5.47 per thing-a-ma-bob, how can we determine the minimum number of units to achieve profitability?

Minimum Number of Thing-a-Ma-Bobs for Profitability

To calculate the minimum number of thing-a-ma-bobs that the company must produce and sell to make a profit, we need to compare the revenue with the cost.

The cost function for the company making thing-a-ma-bobs can be determined by adding the start-up cost to the cost per unit of production multiplied by the number of thing-a-ma-bobs produced. The cost function is represented as: C(x) = $39,305 + ($2.40 * x)

The revenue function for the company is calculated by multiplying the selling price of each thing-a-ma-bob by the number of thing-a-ma-bobs sold. The revenue function is represented as: R(x) = $5.47 * x

To find the minimum number of thing-a-ma-bobs needed for profitability, we set up the inequality: R(x) > C(x)

Substituting the revenue and cost functions into the inequality, we have: $5.47 * x > $39,305 + ($2.40 * x)

Solving the inequality, we isolate the x term: $3.07 * x > $39,305

Dividing both sides by $3.07, we get: x > 12,809.48

Since we cannot produce a fraction of a thing-a-ma-bob, the minimum number required for profitability is 12,810 units.