Question

A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p equals 70 minus 0.1 Upper Dp=70−0.1D ​(D is the demand or quantity sold per month and p is the price in​ dollars). The fixed cost is ​$1 comma 5001,500 per month and the variable cost is ​$3535 per unit produced. a. What is the maximum profit per month for this​ product?

Answer 1

max profit at MR = MC is 1,562.5 dollars

Step-by-step explanation:

we need to solve for the point at which MR = MC

First we calculate marginal revenue, the revenue generate from an additional units which, is the slope of the revenue function

p = 70 - 0.1Q

total revenue = (70 - 0.1Q)Q = -0.1Q^2 + 70Q

dR/dq= -0.2q + 70

Then we do the same for marginal cost, the cost to produce another unit:

total cost: 1,500 + 35 Q

dC/dq = 35

Now we equalize and solve:

-0.2q + 70 = 35

70 - 35=0.2q

35/0.2 = q = 175

p = 70 - 0.1 (175) = 70 - 17.5 = 52.5

52.5Q - 1,500 - 35Q = profit

52.5 x 175 - 1500 - 35 x 175 = profit

profit = 1562.5

if we calcualte for one up or down:

Q = 174 then profit = 1562.4

Q = 176 then profit = 1562.4

This profit is lower than our maximize point, so we agree this is the max point.