Network
Let's calculate the maximum profit step by step:
Total Revenue (TR): TR = P * Q TR = 100 * Q
Total Cost (TC): TC = 200 + 2Q^2
Profit (π): π = TR - TC π = 100Q - (200 + 2Q^2) π = -2Q^2 + 100Q - 200
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: π' = -4Q + 100 -4Q + 100 = 0 -4Q = -100 Q = 25.
Now that we have the quantity (Q) that maximizes profit, we can calculate the maximum profit by substituting Q = 25 into the profit function: π = -2(25)^2 + 100(25) - 200 π = -1250 + 2500 - 200 π = 1050
So, the maximum profit received by the producer is 3550.
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