Question

Yaster Gadgets manufactures and sells x smartphones per week. The weekly price- demand and cost equations are, respectively,

p=516-0.37 x and C(x) = 19,278 + 19 x.
Suppose Yaster Gadgets wants to maximize weekly profit. Compute the following quantities.
1. What price should Jesaki charge for the phones? $ per phone. Round to the nearest cent.
2. How many phones should be produced each week? phones. Round to 2 decimal places.
3. What is the maximum weekly profit? $_ per week. Round to the nearest cent.
Enter the result for 2.
____

Answer 1

Optimal pricing and output for Yaster Gadgets require finding where marginal revenue equals marginal cost, using the given price-demand and cost equations, and calculating the maximum profit from these values.

Step-by-step explanation:

The student is tasked with determining the price, the number of smartphones to produce, and maximum weekly profit for Yaster Gadgets. To solve this problem, one would typically take the revenue function (price times quantity) and subtract the cost function to get a profit function.

The profit function would then be differentiated with respect to the number of smartphones, and set equal to zero to find the critical points. Since the given functions are linear, the point where marginal revenue equals marginal cost will give us the optimal number of smartphones to produce for maximum profit.

We are given the price-demand equation p = 516 - 0.37x and the cost function C(x) = 19,278 + 19x. The profit function would be Profit(x) = px - C(x). After determining the optimal value of x, we plug it back into the price-demand equation to get the optimal price, and finally calculate the maximum weekly profit.