Answer:
max profit at MR = MC is 1,562.5 dollars
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.
