Question

PLEASE SHOW HOW TO GRAPH ON EXCEL. I DONT KNOW HOW TO GRAPH IT. please also solve as instructed in problem

• B.5 The Attaran Corporation manufactures two electrical products: portable air conditioners and portable heaters. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each heater must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each heater assembled may be sold for a $15 profit. Formulate and solve this LP production-mix situation, and find the best combination of air conditioners and heaters that yields the highest profit. PX

Answer 1

Let 'A' and 'H' denote the number of AC and Heaters respectively.

Max Z = 25 A + 15 H
s.t.
3A + 2H <= 240 (wiring time)
2A + 1H <= 140 (drilling time)
A, H >= 0

In Excel, repeat the following table, select it (as shown)

=25*15 3A +2H = 240 2A + 1H <= 140 =(240-3*B3)/2 =140-2*B3 =(240-3*B4)/2 =140-2*B4 =(240-3*B5)/2 =140-2*65 =(240-3*B6)/2 =140-2*B6 =(240-3*87)/2 =140-2*B7 =(240-3*88)/2 =140-2*88 =(240-3*89)/2 =140-2*89 =(240-3*B10)/2 =140-2*810 =(240-3*B11)/2 =140-2*311 Isoprofit line =($F$2-25*83)/15 =($F$2-25*84)/15 =($F$2-25*85)/15 =($F$2-25*16)/15 =($F$2-25*87)/15 =($F$2-25*88)/15 =($F$2-25*39)/15 =($F$2-25*310)/15 =($F$2-25*311)/15

Then go to Insert --> Scatter --> Scatter with smoothed line

We will get this:

-3A +2H<= 240 -2A +1H<= 140 - Isoprofit line 20 40 60 80 100

Then mark the feasibility area (manually inserting 'shapes') and move the isoprofit line away from the origin (mentally).

40,60 -3A +2H<= 240 - 2A +1H<= 140 - Isoprofit line - 20 40 60 80 100

The point at which the isoprofit line leaves the feasibility region is (40, 60) and the optimal solution is:

A = 40
H = 60
Max Z = 25*40 + 15*60 = 1900