Question

In: Operations Management

Please answer all 4 parts of this question. Hervis Car Rental in Austin, Texas, has 50...

Please answer all 4 parts of this question.

Hervis Car Rental in Austin, Texas, has 50 high-performance Shelby-H Mustangs in its rental fleet. These cars will be in greater demand than usual during the last weekend in July when the Central Texas Mustang Club holds its annual rally in Austin. At times like this, Hervis uses a revenue management system to determine the optimal number of reservations to have available for the Shelby-H cars.

Hervis has agreed to have at least 60% of its Shelby-H Mustangs available for rally attendees at a special rate. Although many of the rally attendees will request a Saturday and Sunday two-day package, some attendees may select a Saturday-only or a Sunday-only reservation. Customers not attending the rally may also request a Saturday and Sunday two-day package, or make a Saturday-only or Sunday-only reservation. Thus, six types of reservations are possible. The cost for each type of reservation is shown here.

	Two-Day	Saturday-	Sunday-
	Package	Only	Only
Rally	$125	$75	$65
Regular	150	85	75

The anticipated demand for each type of reservation is as follows:

	Two-Day	Saturday-	Sunday-
	Package	Only	Only
Rally	20	10	15
Regular	10	20	25

Hervis Car Rental would like to determine how many Shelby-H Mustangs to make available for each type of reservation in order to maximize total revenue.

Define the decision variables.
Define the objective function.
Define the constraints.
Determine an optimal solution.

Expert Solution

(a)

Define the decision variables as follows:

	Two-Day	Saturday-	Sunday-
	Package	Only	Only
Rally	X11	X12	X13
Regular	X21	X22	X23

So, for example, X11 = No. of cars for Rally in a two-day package

(b)

Objective function:

Max Z = 125 X11 + 75 X12 + 65 X13 + 150 X21 + 85 X22 + 75 X23

(c)

Constraints:

X11 + X12 + X13 >= 60% of 50 i.e. 30

X11 + X12 + X13 + X21 + X22 + X23 <= 50

X11 <= 20

X12 <= 10

X13 <= 15

X21 <= 10

X22 <= 20

X23 <= 25

Xij >= 0

(d)

LINDO Code:

Max 125 X11 + 75 X12 + 65 X13 + 150 X21 + 85 X22 + 75 X23
s.t.
X11 + X12 + X13 > 30
X11 + X12 + X13 + X21 + X22 + X23 < 50
X11 < 20
X12 < 10
X13 < 15
X21 < 10
X22 < 20
X23 < 25
end

Solution:

keosha answered 2 months ago

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