This leaves 50 hours of labor, and 12 hours of finishing to do side work.

They don’t have enough labor to finish two dining rooms so they can either make two kithen suites, or one of each. Since one of each is more profitable then making two kitchen ones then to maximize profit he should make one unit of each in the alloted time netting an extra $840, and saving him an extra 2 hours of finishing in the process (makeing two kitchens while making less profit also takes 2 more finshing hours)

But before applying the suggested approach, we should first layout the contraints. Since McNamara has a fixed contract with a firm, we should deduct from the 300 workers hours available for assembly the hours needed to assemble both the 5kitchen and 3dining, which will leave us with only 110 hours for assembly(first constraint). We should also deduct from the 72 hours available for finishing the hours needed for 5kitchen and 3 dining, leaving us with only 57 hours(second constraint). The second constraint, however, will be immaterial as all possible mix of products,considering only the first constraint, will always provide unutilized finishing hours.

Trial and error

Let K = Kitchen (20 hrs)

D = dining (30 hrs)

1 K and 4 D

110=1(20) + 4(30)

110=130, thus, beyond the limit

2 K and 3 D

110=2(20) + 3(30)

110=130, beyond the limit

3 K and 2 D

110=3(20) +2(30)

110=120, beyond the limit

4 K and 1 D

110=4(20) + 1(30)

110=110, possible answer

profit = 4(360) + 1(480) = 1920

5K and 0 D

110=5(20)

110=100, possible answer

profit = 5(360) = 1800

Thus 4K and 1D will maximize profit. 1920 plus the profit derived from the fixed contract of 3240 [5(360)+3(480)], my suggested answer will be 5,160.

to maximize profit, do your own homework