A company manufactures Products A, B, and C. Each product is processed in three departments: I, II, and III. The total available labor-hours per week for Departments I, II, and III are 900, 1080, and 840, respectively. The time requirements (in hours per unit) and profit per unit for each product are as follows. (For example, to make 1 unit of product A requires 2 hours of work from Dept. I, 3 hours of work from Dept. II, and 2 hours of work from Dept. III.) Product A Product B Product C Dept. I 2 1 2 Dept. II 3 1 2 Dept. III 2 2 1 Profit $24 $16 $20 How many units of each product should the company produce in order to maximize its profit

The company should produce 1980 units of product B and 840 units of product C to maximize its profit (no units should be produced of product A)

Step-by-step explanation:

Each department time cost for each product is a number divisible of 6. We can see how much profit each department obtains with each product in 6 hours making only that.

Department 1:

Product A: since it takes 2 hours to make this product, then in 6 hours it would make 3. The profit is 3*24 = $72

Product B: It takes only 1 hour to make, thus in 6 hours dep 1 can produce 6. The profit is 6*16 = $96

Product C: it takes 2 hours to make, thus dep 1 makes 3 units in 6 hours, giving a profit of 3*20 = $60.

Department 2:

Product A: It takes 3 hours to make, therefore in 6 hours it will be able to make just 2 units, giving a profit of 2*24 = $48

Product B: The profit is the same than in Dep 1, since the time cost per unit is equal. The profit is $96

Product C:  The profit is the same than in Dep 1, since the time cost per unit is equal. The profit is &60

Department 3:

Product A:  The profit is the same than in Dep 1, since the time cost per unit is equal. The prodit is $72

Product B: This department makes 3 units of product B in 6 hours, because it takes 2 hours to make one unit instead of 1. The profit is 3*16 = $48

Product C: Since it takes only 1 hour to make 1 unit, then in 6 hours it can make 6. The profit is 6*20 = $120

Whit this information, we conclude that department 1 and department 2 are more cost efficient at producing product B and department 3 is more cost efficient at producing product C. In all the cases, each department takes 1 hour to produce one unit of its most cost efficient product, as a result

We conclude that the company should produce 900+1080 = 1980 units of product B and 840 units of product C to maximize its profit.