A small firm makes three products, which all follow the same three-step (milling, inspection, and drilling) process. Product A requires 6 minutes of milling, 5 minutes of inspection, and 4 minutes of drilling; product B requires 2.5 minutes of milling, 2 minutes of inspection, and 2 minutes of drilling; and product C requires 5 minutes of milling, 4 minutes of inspection, and 8 minutes of drilling. The firm has 20 hours available during the next period (next week) for milling, 15 hours for inspection, and 24 hours for drilling. Product A contributes $6.00 per unit to profit, product B contributes $4.00 per unit, and product C contributes $10.00 per unit. 1 hour has 60 minutes. The firm needs to determine the quantities of product A, B, and C, with a goal of maximizing the total profit.

At the optimum solution, what is the company's profit during the next period?

How many units of each are produced at the optimal solution (use numbers) ?

At the optimum solution, what is the company's profit during the next period?

$2,070

How many units of each are produced at the optimal solution (use numbers) ?

180 units of product B 135 units of product C

Explanation:

Milling Inspection Drilling C. M.

Product A 6 5 4 $6

Product B 2.5 2 2 $4

Product C 5 4 8 $10

total time 1,200 900 1,440

Contribution margin per minute

Milling Inspection Drilling Total

Product A $1 $1.20 $1.50 $3.70

Product B $1.60 $2 $2 $5.60

Product C $2 $2.50 $1.25 $5.75

Even though product C has a higher contribution margin, its total production will be contrained by Drilling, since only 180 units can be completed ( = 1,440 hours / 8 hours per unit) profits will equal $1,800.

So we must continue with product B which has the second highest contribution margin per minute with a maximum production of 450 units (Milling is the constraint). This would result in a total profit of $1,800.

The maximum production of product A is also 180 units (inspection is the constraint), which would generate only $1,080 in profits. So we can eliminate product A from the analysis.

Now we need to determine which combination of products B and C should be produced.

If we produce 180 units of product B and 135 units of product C, our total profits will be (180 x $4) + (135 x $10) = $2,070

total number of machine hours employed:

Milling Inspection Drilling

Product B 450 360 360

Product C 675 540 1,080

total 1,125 900 1,440

only 75 hours of Milling will be idle under the production schedule.