The inverse demand curve a monopoly faces is p=130 - Q

Demand Function

P = 130 - Q

Marginal revenue can be calculated from the demand function by doubling the coefficient of Q

Marginal Revenue Function

MR = 130 - 2Q

Cost Function

TC = 20 + 5Q

Marginal cost can be calculated from the cost function by differentiation

MC = dTC / dQ

MC = 5

Profit is maximized where marginal revenue and marginal cost both are equal.

Equating MR and MC

130 - 2Q = 5

130 - 5 = 2Q

Q = 62.5

Hence the profit-maximizing quantity is 62.5 units

Price can be calculated from the demand function by using this quantity.

P = 130 - Q

P = 130 - (62.5)

P = 67.5

Hence the profit-maximizing price is $67.5