Question: Roberto owns a price-taking computer repair firm. His cost function is \(C\left( Q \right)=10Q+0.25{{Q}^{2}}\) ,and his marginal cost function is \(MC\left( Q \right)=10+0.5Q\), where Q is the number of computers his shop repairs.

a. If Roberto can charge $20 for a repair, how many repairs should he do? What is his profit?

b. If Roberto can charge $10 for a repair, how many repairs should he do? What is his profit?

c. If Roberto can charge $30 for a repair, how many repairs should he do? What is his profit?