If we let x represent the number of units sold and P the total profit, then, with a profit of $12 per unit, assuming that 6 hours are required to produce each unit and only 60 hours of production time are available per week, the following mathematical model defines the total profit earned by selling x units: Max 10x
5x <=90
x>0

Suppose the firm in this example considers a second product that has a unit profit of $7 requires 3 hours of production time for each unit produced. use y as the number of units of product 2 produced.

a. Show the mathematical model when both products are considered simultaneously. Express your answers in terms of x and y.
b. Identify the controllable and uncontrollable inputs for this mode.