Harry's Hardware is a small business that sells bags of cement in a perfectly competitive market. The cost function of the business is: TC (q) = 22 + 5Q + 0,05q^2 where is the amount of bags of cement produced. The current price of cement is £10 per bag.
a) Using formal mathematical notation, express Harry's Hardware's problem, assuming that its managers want to maximise profit.
b) Solve the Harry's Hardware's problem to determine the number of bags of cement that maximises profit. Also, calculate and report the maximum profit that Harry's Hardware can achieve.