a. The profit from the linear programming model and the associated
variables are:
Profit =1986
A

B

C

D

E

F

71.4

100

243

171

514

343

b. Machines 2 ane 3 have nonzero shadow prices and are limiting
the companies profit. Also the market of product B is limiting.
c. The shadow price of Mach. 2 is 0.64. Although the range
on this right side allows only an increase of 100 with this
unit value, it is upper bound on larger increases. The change
in profit is limited from above by 1500*.64 = 1542. This does
not pay back the added cost of $1600 per week, so the change
is not justified.
d. Add a new variable, B2, with the same requirements of
B, except the revenue is 19. The solution finds B2 = 0, so there
is no need to enter the additional market.
e.
The solution buys 100 hours of time on M2 with no extra time
on the other machines.
Profit= 1995
A

B

C

D

E

F

50

100

300

150

550

400

f. Goal Programming formulation:
