SOLUTION: You are thinking of making your home more energy efficient by replacing some of the light bulbs with compact fluorescent bulbs and insulating part or all of your exterior walls. Ea

Let  X = the number of compact fluorescent light bulbs and 

let  Y = "how many square feet of insulation should you purchase".


Then the "energy money" you will save per year is 2X + 0.2Y.
It is your "objective function"  Z = 2X + 0.2Y.


The restrictions are:

4X + 1Y <= 1200   dollars   (1)   (<<<---=== money restriction)

0 <= X < = 50               (2)   (<<<---=== the number of bulbs)

0 <= Y <= 1100              (3)   (<<<---=== square feet)


Your feasibility area is shown in the Figure below:


    


    Plot  4X + Y = 1200 (red),  Y= 1100 (green)  and  X= 50 (blue)


Using the LP-method, you should check the objective function in the corner points of the feasibility area:


     P1 = ( 0,1100)
     P2 = (25,1100)
     P3 = (50,1000)
     P4 = (50,0)


You have 

    at P1  Z = 2*0   + 0.2*1100 = 220

    at P2  Z = 2*25  + 0.2*1100 = 270

    at P3   Z = 2*50 + 0.2*1000 = 300

    at P4   Z = 2*50 + 0.2*0    = 100.


Thus the point P3 = (50,1000) gives the maximum saving.  It means that 50 bulbs and 1000 feet insulation is the solution.

Your expected annual energy saving will be 300 dollars.


By the way, your spending will be  4*50 + 1*1000 = 1200 dollars.


Answer.  The optimal solution is  50 bulbs and 1000 square feet insulation.

         Your expected annual energy saving will be 300 dollars.