Question

Evans:

Evans Enterprises has bought a prime parcel of beachfront property and plans to build a luxury hotel. After meeting with the architectural team, the Evans family has drawn up some information to make preliminary plans for construction. Excluding the suites, which are not part of this decision, the hotel will have four kinds of rooms: beachfront non-smoking, beachfront smoking, lagoon view non-smoking, and lagoon view smoking. To decide how many of each of the four kinds of rooms to plan for, the Evans family will consider the following information.

After adjusting for expected occupancy, the average nightly revenue for a beachfront non-smoking room is $175. The average nightly revenue for a lagoon view non-smoking room is $130. Smokers will be charged an extra $15.

Construction costs vary. The cost estimate for a lagoon view room is $12,000 and for a beachfront room is $15,000. Air purifying systems and additional smoke detectors and sprinklers ad $3000 to the cost of any smoking room. Evans Enterprises has raised $6.3 million in construction guarantees for this portion of the building.

There will be at least 120 but no more than 180 beachfront rooms.

Design considerations require that the number of lagoon view rooms be at least 1.5 times the number of beachfront rooms, and no more than 2.5 times that number.

Industry trends recommend that the number of smoking rooms be no more than 50% of the number of non-smoking rooms.

There should be at least 45 rooms of each kind.

What is the optimal solution?

What is the optimal value of the objective function?

For what values of the objective coefficient will the above solution be valid? Include ranges for all decision variables.

If the budget increases to 7 million what is the change in the objective function? What is the shadow price for budget?

Answer 1

Create Excel model as follows:

Enter Solver Parameters as shown below:

Click Solve to generate the solution.

After that, values appear automatically in yellow cells

On the Solution Results window, check Sensitivity and Click OK to generate sensitivity report

Sensitivity report:

Optimal solution:

Number of Beachfront Non-smoking rooms (BN) = 135

Number of Beachfront Smoking rooms (BS) = 45

Number of Lagoon View Non-smoking rooms (VN) = 232.5

Number of Lagoon View Smoking rooms (VS) = 45

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Optimal value of the objective function = Total revenue

= $ 68,925

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Ranges for objective function coefficients of all variables is obtained by adding allowable increase and subtracting allowable decrease from objective coefficient.

Variable	Lower limit	Upper limit
BN	162.5	Infinity
BS	-Inifinity	207.5
VN	116	140
VS	-Inifinity	162.5

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Shadow price of budget is 0.010833

If budget is increased to $ 7 million, then increase = 7 - 6.3 = $ 0.7 million. it will remain in feasible range, because allowable increase for this constraint is 2,070,000  (2.7 million)

Therefore, shadow price is applicable for this change.

Change in objective function = Shadow price times change

= 0.010833* $ 0.7 million

= $ 7,583.33 (increase in total revenue)