To find the profit-maximizing level of output, we need to find the level of output where total revenue (TR) is equal to total cost (TC).

TR = TC 8Q - 3 = Q^2 + 2Q + 2

Rearranging the equation: Q^2 + 2Q + 2 - 8Q + 3 = 0 Q^2 - 6Q + 5 = 0

Factoring the quadratic equation: (Q - 5)(Q - 1) = 0

Setting each factor equal to zero: Q - 5 = 0 or Q - 1 = 0

Solving for Q: Q = 5 or Q = 1

So, the profit-maximizing level of output is either Q = 5 or Q = 1.

To find the maximum profit, we substitute the profit-maximizing level of output into the total profit function (π = TR - TC).

For Q = 5: TR = 8(5) - 3 = 37 TC = (5)^2 + 2(5) + 2 = 37 π = 37 - 37 = 0

For Q = 1: TR = 8(1) - 3 = 5 TC = (1)^2 + 2(1) + 2 = 5 π = 5 - 5 = 0

Therefore, the maximum profit is 0.