The demand curve for the toys is p 10 q2 where q is the nu

The demand curve for the toys is p = 10 q² , where q is the number of toys produced in millions. It costs the company $3.75 to make a toy. The company produces 2 million toys at present and makes a profit of $4,500,000, but is desirous of reducing production. What number of toys could the company produce to generate the same profit?

Solution

Total revenue = pq

R = 10q - q^3 million dollars

C = 3.75q million dollars

Total profit = R - C

P = 10q - q^3 - 3.75q

P = -q^3 + 6.25q million dollars

Now, it is given that the profit = 4500000, i.e 4.5 million, so plug in P = 4.5

-q^3 + 6.25q = 4.5

Solving, we get q = 2 , 0.802776 as the positive solutions

So, approx 0.802776 million or 802776 toys will also generate the same profit

ANS ---> 802776 toys