Network
The total profit (π) is given by the difference between total revenue (TR) and total cost (TC): π = TR - TC
Substitute the given TR and TC functions: π = (25Q - 1.5Q^2) - (20 + 4Q) π = 25Q - 1.5Q^2 - 20 - 4Q π = -1.5Q^2 + 21Q - 20
To find the quantity (Q) that maximizes profit, take the derivative of the profit function with respect to Q, set it to zero, and solve for Q: d(π)/dQ = -3Q + 21 0 = -3Q + 21 3Q = 21 Q = 7
Substitute Q = 7 into the profit function to find the maximum profit: π = -1.5(7)^2 + 21(7) - 20 π = -1.5(49) + 147 - 20 π = -73.5 + 147 - 20 π = 53.5
So, the maximum profit obtained by the producer is 53.5. Therefore, the correct option is: • 53.5
***
