5. Marlene offers an aerobics class on Mondays, Tuesdays, Wednesdays, Fridays an
ID: 454453 • Letter: 5
Question
5. Marlene offers an aerobics class on Mondays, Tuesdays, Wednesdays, Fridays and Saturdays. She teaches three types of aerobics classes, Jazzercise, Step aerobics, and Zumba. In the past, she primarily randomly picked a class for a given day. However now that she has plenty of data, she has decided to use LP to determine which type of class should be offered each day. Based on the past data, she averaged the profits for each class according to the day in which the course was taught. For instance, the average profit when Jazzercise was taught on Mondays was $80. She is concerned that if a course if offered to often the revenue will decrease, thus she has decided not to offer any course more than twice a week. Only one class can be offered each day. Formulate the LP problem to maximize profit.
Jazzercise
Step Aerobics
Zumba
Monday
80
70
60
Tuesday
60
60
50
Wednesday
50
50
70
Friday
60
55
60
Saturday
90
80
100
5a. On which day(s) should Zumba be offered? ______________________ 5b. How much would the average profit on Step aerobics have to increase before it would be beneficial to offer the class on Monday? ____________ 5c. What would be the expected profit if she could only offer Jazzercise only once a week? ____________ 5d. Demonstrate if the solution would change if the profit for Zumba decreased by 5% on Fridays and Saturdays. 5e. Would it be beneficial to increase the number of days Step aerobics could be offered? Provide support for your answer.
Jazzercise
Step Aerobics
Zumba
Monday
80
70
60
Tuesday
60
60
50
Wednesday
50
50
70
Friday
60
55
60
Saturday
90
80
100
Explanation / Answer
Decision variables are suppose to represent which class on which day. Let us represent decision variables as Xij representing jth type class on ith day. Monday=1, Tuesday=2, Wednesday=3...for j, .Jazzercise=1, Step aerobics=2, and Zumba=3. Xij takes the value=1 if class is held otherwise its value is zero.
Objective function is Maximize Profit = Double summation CijXij where Cij is profit corresponding to Xij
Constraints:
Given that only one class per day and maximum two classes of same course during the week given as:
Sigma(for fixed i and j varying) Xij = 1 and Sigma (for fixed j and i varying) Xij <= 2
Solution obtained using Excel solver is as mentioned above:
5a. On which day(s) should Zumba be offered? __Wednesday and Saturday____________________
5b. How much would the average profit on Step aerobics have to increase before it would be beneficial to offer the class on Monday? $90
5c. What would be the expected profit if she could only offer Jazzercise only once a week? $350
5d. Demonstrate if the solution would change if the profit for Zumba decreased by 5% on Fridays and Saturdays.
5e. Would it be beneficial to increase the number of days Step aerobics could be offered? Provide support for your answer.
Objective co-effcients Jazzercise Step Aerobics Zumba Monday 80 70 60 Tuesday 60 60 50 Wednesday 50 50 70 Friday 60 55 60 Saturday 90 80 100 Decision variables Jazzercise Step Aerobics Zumba Sum Constraint Monday 1 0 0 1 1 Tuesday 0 1 0 1 1 Wednesday 0 0 1 1 1 Friday 1 0 0 1 1 Saturday 0 0 1 1 1 Sum 2 1 2 Constraint 2 2 2 Value of Objective Max. Profit= 370Related Questions
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