I thinks i got the problem right this time

P=MR=$750
TC =2,500,000+500q+0.005Q^2 (squared)
Mc =500+0.01Q

Calculate profit maximizing level
Calculate the company's optimal profit and optimal profit as a percentage of sales revenue

Can anyone help here I am lost

Sure, I can help you with that! To find the profit-maximizing level, we need to determine the quantity where Marginal Revenue (MR) equals Marginal Cost (MC).

Given:
P = MR = $750
TC = 2,500,000 + 500q + 0.005Q^2 (squared)
MC = 500 + 0.01Q

Step 1: Find the quantity where MR equals MC:
Setting MR equal to MC:
750 = 500 + 0.01Q

Rearranging the equation:
0.01Q = 750 - 500
0.01Q = 250
Q = 250 / 0.01
Q = 25,000

So, the profit-maximizing level of quantity (Q) is 25,000 units.

Step 2: Calculate the company's optimal profit:
To calculate the optimal profit, we need to subtract the total cost from the total revenue at the profit-maximizing level of quantity.

TR (Total Revenue) = P × Q
TR = $750 × 25,000
TR = $18,750,000

TC (Total Cost) = 2,500,000 + 500Q + 0.005Q^2
TC = 2,500,000 + 500(25,000) + 0.005(25,000)^2
TC = 2,500,000 + 12,500,000 + 3,125,000
TC = 18,125,000

Optimal Profit = TR - TC
Optimal Profit = $18,750,000 - $18,125,000
Optimal Profit = $625,000

Step 3: Calculate the optimal profit as a percentage of sales revenue:
Optimal Profit as a Percentage of Sales Revenue = (Optimal Profit / Total Revenue) × 100
Optimal Profit as a Percentage of Sales Revenue = ($625,000 / $18,750,000) × 100
Optimal Profit as a Percentage of Sales Revenue = 3.33%

Therefore, the company's optimal profit at the profit-maximizing level is $625,000, and it represents approximately 3.33% of the sales revenue.