Explain it step by step rather than recopy , explain the theory and how the answer was derived, thanks

Willingness to pay (E1005) 50 MC 25 5 0 50 100 Local park land (acres) To find the optimal size of local parks, equate the aggregate willingness to pay P = 50 - 1/2 Q and the marginal cost MC = 1/2Q to find Q = 50 acres.Ten identical consumers all have individual willingness-to-pay curves P = 5 - 20 Q for a public good-say, local parks (where P is measured in hundreds of euros and Q is measured in acres). Construct and graph the aggregate willingness-to-pay curve. For 50 acres of parks, what is the maximum each individual would be willing to pay? If the marginal cost of providing parks measured in hundreds of euros is MC = =Q, what is the optimal size of local parks? ANSWER: The maximum each individual is willing to pay is the area under his W.T.P. curve up to Q = 50. At Q = 50, w.t.p. = 2.5 so maximum willingness to pay for all 50 units equals 2.5(50) + 1/2(5-2.5)50 = 125 + 62.5 = 187.5. For all ten consumers this sums to (1875