A factory manufactures three products, A, B, and C. Each product requires the use of two machines, Machine I and Machine II. The total hours available, respectively, on Machine I and Machine II per month are 7,170 and 8,230. The time requirements and profit per unit for each product are listed below. A B C Machine I 5 9 12 Machine II 7 8 15 Profit $9 $13 $16 How many units of each product should be manufactured to maximize profit, and what is the maximum profit? Start by setting up the linear programming problem, with A, B, and C representing the number of units of each product that are produced.

To determine the number of units of each product that should be manufactured to maximize profit, we can use linear programming. We'll set up a mathematical model and solve it. Let's define the variables: Let x, y, and z represent the number of units of products A, B, and C, respectively. The objective is to maximize the profit, which is given by: Profit = 9x + 13y + 16z Subject to the following constraints: 5x + 9y + 12z ≤ 7,170 (Machine I constraint) 7x + 8y + 15z ≤ 8,230 (Machine II constraint) x, y, z ≥ 0 (Non-negativity constraint) We can solve this linear programming problem using optimization techniques or software. The solution will provide the optimal values of x, y, and z, as well as the maximum profit.