Question

You and your roommate are passionate about designing customized T-shirts, and you plan on opening an online store to sell them. Your roommate knows you took BUAD 311 last semester so he assigns you to oversee pricing. Based on sales data from similar online T-shirt stores, you estimate demand to be a function of the price p:

D(p) = 600 - 15p, 0<=p<=40.
It costs $2 to produce each T-shirt.
For a "single-price" policy, what is the optimal price to set in order to maximize the total profit? What is the optimal profit?

Answer 1

The optimal price to maximize profit is $35.29, and the optimal profit is $3,527.

Step-by-step explanation:

To find the optimal price and profit for a single-price policy, we need to determine the quantity that maximizes profit. First, we set the demand function equal to the cost function to find the quantity: 600 - 15p = 2p. Simplifying this equation, we get 600 = 17p, and solving for p, we find p = 35.29. So, the optimal price to set is $35.29. To find the optimal profit, we substitute this price into the demand function to find the quantity: D(p) = 600 - 15(35.29), which gives us a quantity of 100.86 (rounding down to 100). The profit is then calculated by subtracting the cost per unit from the price and multiplying by the quantity: profit = (35.29 - 2) * 100 = $3,527.