The demand for the company’s products is determined by the formula: Qd = 5000-2P. The total costs of this company

The demand for the company’s products is determined by the formula: Qd = 5000-2P. The total costs of this company are related to the number of products manufactured as follows: С = 3Qs ^ 2 + 8Qs + 60,000. Determine: a) max profit of the company; b) how many units of product will it produce? ; c) at what price will the firm sell its products?

Solution:
P = TR-TC = P * Q-3 * Q ^ 2-8 * Q-60,000 – firm profit;
dП / dQ = P-6 * Q-8 = 0 => P = 6 * Q + 8;
Q = 5000-2 * (6 * Q + 8) => 5000-13 * Q-16 = 0 => Q = (5000-16) / 13 = 383.385 how many units of product it will produce at the same time;
P = 6 * 383.385 + 8 = 2308.308 at this price it will sell products (monetary units);
1) TC = 3 * 383.385 ^ 2 + 8 * 383.385 + 60,000 = 146984.058 + 3067.08 + 60,000 = 210051.138 – the value of total costs;
2) FC = 3 * 383.385 ^ 2 + 8 * 383.385 = 146984.058 + 3067.08 = 150051.138 – the value of variable costs;
3) CC = 60,000 – the amount of fixed costs;
Pmax = 2308.308 * 383.385-210051.138 = 674919.525 is the maximum profit of the company.