Island Publishing Company publishes two types of magazines on a monthly basis: a

Question

Island Publishing Company publishes two types of magazines on a monthly basis: a restaurant and entertainment guide and a real estate guide. The company distributes the magazines free to businesses, hotels, and stores on Hilton Head Island in South Carolina. The company's profits come exclusively from the paid advertising in the magazines. Each of the restaurant and entertainment guides distributed generates $0.50 per magazine in advertising revenue, whereas the real estate guide generates $0.75 per magazine. The real estate magazine is a more sophisticated publication that includes color photos, and accordingly it costs $0.25 per magazine to print, compared with only $0.17 for the restaurant and entertainment guide. The publishing company has a printing budget of $4,000 per month. There is enough rack space to distribute at most 18.000 magazines each month. In order to entice businesses to place advertisements. Island Publishing promises to distribute at least 8.000 copies of each magazine. The company wants to determine the number of copies of each magazine it should print each month in order to maximize advertising revenue. Formulate a linear programming model for this problem. Solve the model graphically. Determine the sensitivity range for the advertising revenue generated by the real estate guide. Does the company spend all of its printing budget? If not. how much slack is left over? What would be the effect on the optimal solution if the local real estate agents insisted that 12.000 copies of the real estate guide be distributed instead of the current 8.000 copies, or they would withdraw their advertising? Solve the model using the software (such Undo or Excel). How much would it be worth to Island Publishing Company to obtain enough additional rack space to distribute 18.500 copies instead of the current 18.000 copies? 20.000 copies? How much would it be worth to Island Publishing to reduce the requirement to distribute the entertainment guide from 8.000 to 7.000 copies?

Explanation / Answer

Problem is

Entering =X2=X2, Departing =S4=S4, Key Element = 11

R4R4 (new) =R4=R4(old)

R1R1 (new) =R1=R1 (old) 0.17R4-0.17R4 (new)

R2R2 (new) =R2=R2 (old) R4-R4(new)

R3R3(new) =R3=R3 (old)

Entering =X1=X1, Departing =S3=S3, Key Element = 11

R3R3 (new) =R3=R3(old)

R1R1 (new) =R1=R1 (old) 0.25R3-0.25R3 (new)

R2R2 (new) =R2=R2 (old) R3-R3(new)

R4R4(new) =R4=R4 (old)

Since all CjZj0Cj-Zj0,

Optimum Solution is arrived with value of variables as :
X1=8000X1=8000

X2=8000X2=8000

Maximise Z=10000

MAX Z=Z= 0.50.5 X1+X1+ 0.750.75 X2X2 Subject to constraints 0.250.25 X1+X1+ 0.170.17 X2X2 40004000 11 X1+X1+ 11 X2X2 1800018000 11 X1+X1+ 00 X2X2 80008000 00 X1+X1+ 11 X2X2 80008000 and X1,X20X1,X20

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