How do you solve this Linear Programming problem ?

The factory Oaken Treasures makes two different kinds of chairs, ROCKERS, and SWIVELS . Work on machines A and B is required to make both kinds. Machine A can be run no more than 20 hours a day. Machine B is limited to 15 hours a day. The following chart shows the amount to time on each machine that is required to make one chair. The profit made on each chair is also shown.

Chair Operation A Operation B Profit
Rocker 2 h 3 h $12
Swivel 4 h 1 h $10

1 Answer
Nov 28, 2017

See below.

Explanation:

We have

(("chair", "Op. A", "Op, B" , "Profit"), ("Rocker", t_(RA),t_(RB),c_R), ("Swivel",t_(SA),t_(SB),c_S))

Now

x_R = Number of Rocker's chairs
x_S = Number of Swivel's chairs

t_A = Maximum allowed time for machine A
t_B = Maximum allowed time for machine B

we have

max c_R x_R + c_S x_S

subjected to

t_(RA)x_R+t_(SA)x_S le t_A
t_(RB)x_R+t_(SB)x_S le t_B
x_R ge 0
x_S ge 0

Attached a plot showing in light blue the feasible region and in red the optimal choice with x_R = 2 and x_S = 4

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