Question

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

Answer 1

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`