(See attached file for full problem description)
1. A large sporting goods store is placing an order for bicycles with its supplier. Four models can be ordered: the adult Open Trail, the adult Cityscape, the girl's Sea Sprite, and the boy's Trail Blazer. It is assumed that every bike ordered will be sold, and their profits, respectively, are 30, 25, 22, and 20. The LP model should maximize profit. There are several conditions that the store needs to worry about. One of these is space to hold the inventory. The adult bikes need two feet, but each children's bike needs only one foot. The store has 500 feet of space. There are 1200 hours of assembly time available. The children's bikes need 4 hours each; the Open Trail needs 5 hours and the Cityscape needs 6 hours. The store would like to place an order for at least 275 bikes.
Formulate a model for this problem.
Solve your model with any computer package available to you.
How many of each kind of bike should be ordered and what will the profit be?
Enter the profit ONLY below in the form xxxx or xxxx.0 round to nearest dollar
2. The following data summarizes the historical demand for a product.
Month Actual demand
Use a four period moving average and determine the forecasted demand for September
3. During summer weekdays, boats arrive at the inlet drawbridge according to the Poisson distribution at a rate of 8 per hour. In a 2-hour period,
what is the probability that exactly 10 boats arrive?
Put your answer in the form 0.xxx or .xxx
4. The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code.
low medium high
# of workers compliance compliance compliance
1 50 50 50
2 100 60 20
3 150 70 -10
If he thinks the chances of low, medium, and high compliance are 40%, 20%, and 30%, respectively, what is his expected value of perfect information?
5. To find the optimal solution to a linear programming problem using the graphical method
find the feasible point that is the farthest away from the origin
find the feasible point that is at the highest location>
find the feasible point that is closest to the origin
None of the alternatives is correct
6. Because the dual price represents the improvement in the value of the optimal solution per unit increase in right-hand-side, a dual price cannot be negative.
7. The constraint 2x1 - x2 = 0 passes through the point (400,200).
8. A constraint with a positive slack value
will have a positive dual price
will have a negative dual price
will have a dual price of zero
has no restrictions for its dual price
9. A section of output from The Management Scientist is shown here.
Variable Lower Limit Current Value Upper Limit
1 60 100 120
What will happen to the solution if the objective function coefficient for variable 1 decreases by 20?
Nothing. The values of the decision variables, the dual prices, and the objective function will all remain the same
The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same
The same decision variables will be positive, but their values, the objective function value, and the dual prices will change
The problem will need to be resolved to find the new optimal solution and dual price
10. For any constraint, either its slack/surplus value must be zero or its dual price must be zero.
11. There is a dual price for every decision variable in a model.
12. In the linear programming formulation of a transportation network (Points: 2)
there is one constraint for each node
here is one variable for each arc
the sum of variables corresponding to arcs out of an origin node is constrained by the supply at that node
All of the alternatives are correct
13. The main difference betwen Bayesian and Shafer-Dempster systems of probability is:
Shafer-Dempster is simply not accepted by the mathematical community.
Shafer-Dempster leaves room for future information to fill in present uncertainty.
Bayes has been discredited since it is so old.
Bayes uses past and prior probabilities for updates while Shafer-Dempster uses present and future probabilites.
None of the above are true
14. Use of the Poisson probability distribution assumes that arrivals are not random.
15. The feasible solution is the best solution possible for a mathematical model. (Points: 1)
16. A furniture store has set aside 800 square feet to display its sofas and chairs. Each sofa utilizes 50 sq. ft. and each chair utilizes 30 sq. ft. At least five sofas and at least five chairs are to be displayed.
Suppose the profit on sofas is $200 and on chairs is $100. On a given day, the probability that a displayed sofa will be sold is .03 and that a displayed chair will be sold is .05. Mathematically model the following objective:
Maximize the total expected daily profit.
Max s + c
Max .03s + .05c
Max 6s + 5c
17. If P(A|B) = .2 and P(Bc) = .6, then P(B|A)
cannot be determined
18. The probability of a continuous variable having a specific value is 0.
19. The binomial distribution is appropriate to use to find the probability of the elapsed time between successes.
20. If x is normally distributed with mean 12 and standard deviation 2, then P(x  9) is
P(z  9/10)
P(z  -3/2)
P(z  2/3)
P(z  -3/4)
MCQs on Transportation and probability