. 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 profi t, π, if the fi rm manufactures x pots of paint and sells y pots. (b) Use your formula to calculate the profi t 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 fi rm sells all that it manufactu