Question

Floatway Tours has $420 000 that can be used to purchase new rental boats for hire during the summer. The boats can be purchased from two different manufacturers. Floatway Tours would like to purchase at least 50 boats and would like to purchase the same amount from Sleekboat as from Racer to maintain goodwill. At the same time, Floatway Tours wishes to have a total seating capacity of at least 200.                    

Boat	Manufacturer	Cost	Maximum Seating	Expected Daily Profit
Speedhawk	Sleekboat	$6000	3	$70
Silverbird	Sleekboat	$7000	5	$80
Catman	Racer	$5000	2	$50
Classy	Racer	$9000	6	$110

                                   

Solve this problem and run the sensitivity analysis. Answer the following questions based on the Sensitivity analysis.

Exercise 2

1. Management is interested why they should not order the two models. Explain shortly why they should not order these models. Would the solution change if the Catman’s profit would increase to $60?

2. Management is not sure if their estimate of the profit of the Speedhawk and Classy models are accurate. Management gives new values for the expected daily profits: $80 for Speedhawk and $100 for Classy. Will the optimal solution change? Resolve the problem if needed.

Exercise 3

1. Answer to the following questions based on the Sensitivity analysis (use original problem, with original profits).

• Management is wondering if they should invest $50 000 more to the new boats. Would you recommend it? Explain briefly why or why not.
• What happens if they would need to reduce the budget by $50 000?

2. What is the range of feasibility for constraint “Number purchased”? Explain shorty the meaning of the range in this case. Also, explain why the shadow price is 0.

Exercise 4

1. Management has decided to study what happens if they give up the requirement of purchasing the same number of boats from both manufacturers. Resolve the problem without this constraint.

• How would this decision change the number of boats they will buy, the values of each constraint in the optimal solution point and the maximized profit?
• What would happen if the company would want to buy 56 boats as in the original optimal solution?

2. Management requires that they purchase at least 5 boats of each model. How would this decision change the annual profit?

Answer 1

The model is shown below

The formulas are shown below

The solver parameters are shown below

The result is shown below

The sensitivity report is shown below

Based on these data we will answer the questions

a.

The two models contribute lower to the overall profit contribution for the given budget and seating constraints. For example, if we include silverbird in our mix then the overall daily profit will reduce by $2.

Catman has an allowable increase of 12. This mean as long as the daily profit of Catman is below 72, it will not be recommended.

a.

We can resolve the problem or use the 100% rule test. The value of 100% rule test is (80-70)/45 + (110-100)/16.36 = 0.833

Since the impact is less than 1 the optimal solution will not change even if the daily profits are 80 and 100 for Speedhawk and Classy respectively.

a.

Yes. I would recommend it.

The shadow price of the total cost is 0.012. This means if we spend $1 on total cost, the daily profit will increase by 0.012. This is a daily return of 1.2%. However, if we can operate the boat for 100 days then it will pay for itself.

If they reduce the total spend by 50000 then the solution will change. This is because the feasible region will change. The sensitivity analysis shows an allowable decrease of 45000.

a.

The numbers purchased has a shadow price of 0. This means that this is a non-binding constraint. Even if we remove this constraint, the solution will remain as it is. This means at current feasible region, the constraint on minimum 50 boats have no impact on the solution.