Question

The Desk Company produces two types of desks, traditional and modern. The profit that it makes from a traditional desk is $350. Its profit for each modern desk is $450. The desks are produced using three machines: a drill, a saw and a gluing machine. The hours needed by each desk on each machine are given below. Also given below is the capacity next week in terms of the number of hours available. Finally, marketing considerations require that at least 20% off the desks be traditional and that at least 30% be modern. What should The Desk Company produce

Answer 1

the company should produce 175 modern desks and 404 traditional desks. The profit form this production level = (404 x $350) + (175 x $450) = $141,400 + $78,750 = $220,150

Step-by-step explanation:

some information was missing, so I looked it up:

we have to maximize profit following the equation 350t + 450m

the constraints are:

1.5t + 2m ≤ 1000

3t + 4.5m ≤ 2000

2.5t + 1.5m ≤ 1500

t ≥ 0.2(t + m)

m ≥ 0.3(t + m)

using solver, the result is:

m = 175

t = 404

profit = (404 x $350) + (175 x $450) = $220,150

606 + 350 ≤ 1000 ⇒ 956 ≤ 1000 ✓

1,212 + 787.5 ≤ 2000 ⇒ 1,999.5 ≤ 2000 ✓

1010 + 262.5 ≤ 1500 ⇒ 1,272.5 ≤ 1500 ✓

404 ≥ 0.2 x 579 ⇒ 404 ≥ 115.8 ✓

175 ≥ 0.3 x 579 ⇒ 175 ≥ 173.7 ✓