A factory produces canoes, dinghies, speedboats and catamarans. The resources required are steel, fibreglass, wood and marine paint. The following table shows
the per-unit resource quantities required for each product,
the price we sell each product for,
the per-unit resource prices, and
the resource quantities available to us for purchase:
|Price per unit||$2.00||$2.40||$7.00||$40.00|
After calculating the per-unit profits, we can formulate the linear program to maximise profit as follows:
Max P = 30X1 + 12X2 + 40X3 +
15X2 + 36X3 + 11X4 ≤ 1900.00
27X1 + 4X2 + 4X3 + 64X4 ≤ 900.00
X1 + 2.5X2 + X3 + 13X4 ≤ 55.00
7X1 + 2.1X2 + 2.3X3 + 24X4 ≤ 900.00
Xi ≥ 0.
When this linear program is solved in Excel, the following Sensitivity Report is produced:
Now suppose that the amount of fibreglass available changes to 803.80 units. From the Sensitivity Report, what is the most you can say about the effect on the optimal production plan and profit?
a. The optimal production plan will not change. The optimal profit will be $2177.78.
b. The optimal production plan will change. The optimal profit will be between $2200.00 and $2273.83.
c. The optimal production plan will change. The optimal profit will be between $2200.00 and $2275.28.
d. The optimal production plan will change. The optimal profit will be $2070.47.
e. The optimal production plan will change. The optimal profit will be $2182.03.
f. The optimal production plan will change. The optimal profit will be less than $2039.78.
When we solve the given lpp in excel using solver,
Here rows B2: B4 is obtained by the formula B2= B3*B2; C2= C3*C2; D2= D3*D2 ; E3= E3*E2
F3 is obtained by F3 = B3*B2+ C3*C2 + D3*D2+ E3*E2
F6 = B6*$B$2+C6*$C$2+D6*$D$2+E6*$E$2 and so on.
Using Solver in excel we use the above following values
Data tab > Solver
So we get optimal profit in F6
But now that amount of fibre glass available has changed from 900 to 803.80, our problem will change same way,
Formulating in Solver
As we can see the solution does not change, Therefore optimal production plan will not change. The optimal profit will be $2177.78.
Here is the sensitivity report
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