Revenue earned will be = Demand * Price
Revenue = (6000 - 30P) * PZSK

Total Cost = Fixed Cost + Variable Cost

Total Cost =\(\displaystyle{72000}+{60}\cdot{\left({6000}-{30}{P}\right)}\)

Profit = Revenue - Total Cost

Profit = \(\displaystyle{\left({6000}-{30}{P}\right)}\cdot{P}-{\left({72000}+{60}\cdot{\left({6000}-{30}{P}\right)}\right)}\)

Profit = - \(\displaystyle{30}{P}^{{2}}+{7800}{P}-{432000}\)

Now we have a quadratic equation for Profit. Now its a simple case of maximum value in quadratic equation.

Maximum Value of quadratic equation is at x = \(\displaystyle-\frac{{b}}{{2}}{a}\)

At P = \(\displaystyle-\frac{{7800}}{{{2}\cdot-{30}}}\), we will get max profit

i.e. Price at which max profit, P = R 130

Maximum Profit = R 75000

Total Cost = Fixed Cost + Variable Cost

Total Cost =\(\displaystyle{72000}+{60}\cdot{\left({6000}-{30}{P}\right)}\)

Profit = Revenue - Total Cost

Profit = \(\displaystyle{\left({6000}-{30}{P}\right)}\cdot{P}-{\left({72000}+{60}\cdot{\left({6000}-{30}{P}\right)}\right)}\)

Profit = - \(\displaystyle{30}{P}^{{2}}+{7800}{P}-{432000}\)

Now we have a quadratic equation for Profit. Now its a simple case of maximum value in quadratic equation.

Maximum Value of quadratic equation is at x = \(\displaystyle-\frac{{b}}{{2}}{a}\)

At P = \(\displaystyle-\frac{{7800}}{{{2}\cdot-{30}}}\), we will get max profit

i.e. Price at which max profit, P = R 130

Maximum Profit = R 75000