Question

URBAN PLANNING - URBAN RENEWAL MODEL Example 2.4.6 on page 70 of Taha's book Decision variables: XI-Number of units of single-family homes x2 - Number of units of double-family homes x3 = Number of units of triple-family homes x4 - Number of units of quadruple-family homes xs = Number of old homes to be demolished XS Maximize z=1000 x1 + 1900 x2 +2700 x3 +3400 x4 Subject to .18x1 + 28x2 + 4x3 +.5x4 5.856.25x5) S 300 x3 + x4 25 (x + x2 + x3 + x4) 22(x1 + x2 + x3 + x) > 1 (XI + x2 + x3 + x) 50x1+ 70x2 + 130xi + 160x4 + 2xs s S15000 XI X2 XI, X2, x3, x4 >0 Subject to X5 Maximize z=1000 x1 + 1900 x2 +2700 x3 +3400 x .18x1 + 28x2 + 4x1 + 5x 5.85.25xs) 300 x3 + x4 2.25 (x + x2 + x3 + x) 22 (x1 + x2 + x3 + x4) 21 (x1 + x2 + x3 + x4) 50x1 + 70x2 + 130x5 + 160x4 + 2x < $15000 XI, X2, X3, X4 X5 20 XI X2 Maximize 2 - 1000,+ 190042 + 270043 + 3400 181, +28+ 4x + 3x - 21254s 50 --8, + 2 + 2xy + 2x 1x - 94% + 1xy x 25.x, + 25x - 75 - 75 so 50x704) + 10 +100% + 25 15000

please Solve the question with excel solver

Solve the question with excel solver

Answer 1

The problem is formulated in excel as below. The below 2 images show the formulation as well as the formulas used. The objective function to maximize is highlighted in green and the decision variables are highlighted in yellow.

Post these the solver parameters need to be entered as per the below image.

Once this is done, click on solve. The solver will solve the problem and show the message stating the same. Click on ok. The excel will now have the final solution as per below image.

Thus we can see from above image that the solution is as below

x1 = 36 units of single-family homes

x2 = 98 units of double-family homes

x3 = 45 units of triple-family homes

x4 = 0 units of quadruple-family homes

x5 = 245 units of old homes to be demolished