Two fraternities, Sig Ep and Ep Sig, plan to raise money jointly to benefit homeless people on Long Island. They will sell Yoda vs. Alien T-shirts in the student center, but are not sure how much to charge. Sig Ep treasurer Augustus recalls that they once sold 40 shirts in a week at $7 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 240 per week at $2 per shirt.

Question

Two fraternities, Sig Ep and Ep Sig, plan to raise money jointly to benefit homeless people on Long Island. They will sell Yoda vs. Alien T-shirts in the student center, but are not sure how much to charge. Sig Ep treasurer Augustus recalls that they once sold 40 shirts in a week at $7 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 240 per week at $2 per shirt.

If that is the problem how do i find the REVENUE FUNCTION? and the PROFIT FUNCTION?

Answer 1

Although this is not my area of expertise, I assume the revenue is the amount of income (shirts sold times price).

You cannot find the profit unless you know the original cost of the shirts. Subtract cost from revenue for profit.

I hope this helps. Thanks for asking.

Answer 2

To find the revenue function, you need to multiply the number of shirts sold by the price per shirt.

Let's start with Sig Ep's data. They sold 40 shirts per week at $7 per shirt. Therefore, the revenue function for Sig Ep can be calculated as follows:

Revenue for Sig Ep = Number of shirts sold * Price per shirt = 40 * $7

So, the revenue function for Sig Ep is:

R1(x) = 40x, where x represents the number of shirts sold.

Now, let's move on to Ep Sig's data. They sold 240 shirts per week at $2 per shirt. Hence, the revenue function for Ep Sig can be calculated as:

Revenue for Ep Sig = Number of shirts sold * Price per shirt = 240 * $2

Thus, the revenue function for Ep Sig is:

R2(x) = 480x, where x represents the number of shirts sold.

To find the joint revenue function when both fraternities collaborate, you need to add the revenues of Sig Ep and Ep Sig:

Revenue for both fraternities = Revenue for Sig Ep + Revenue for Ep Sig

R(x) = R1(x) + R2(x) = 40x + 480x

So, the joint revenue function is:

R(x) = 520x, where x represents the number of shirts sold.

To find the profit function, you need to subtract the cost function from the revenue function. However, we don't have the cost information provided in the problem statement. Without the cost data, it is not possible to compute the profit function accurately.