A specialist paint manufacturer receives $12 for each pot sold. The initial set-up cost for the production run is $800 and the cost of making each tin of paint is $3.
(a) Write down a formula for the total profit, π, if the firm manufactures x pots of paint
and sells y pots.
(b) Use your formula to calculate the profit when x = 1000 and y = 800.
(c) State any restrictions on the variables in the mathematical formula in part (a).
(d) Simplify the formula in the case when the firm sells all that it manufactures.