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The Cruise
Their cruise would port out of New Orleans and promised seven days with a panoply of
excursions in Jamaica, Cozumel, and Grand Cayman. A list of excursions at each site
and key features of each appear in the table. The excursions were all day affairs, so it
was possible to engage in only one per port. The cruise ship sailed at night and docked
at each of these three ports at the crack of dawn. By dinner time, the ship was on its
way to the next port and next set of excursions. The couple was energetic and active for
a pair of 52 year-olds., and while enjoying an upper middle class lifestyle, they didn't
want to spend money on excursions that might be better spent on tacky souvenirs. The
couple therefore budgeted $250 for the excursions the prices shown are per couple, so
for example, the $60 will pay for both of them to fill up on jerk chicken and mannish
water.
For each of the duplicate excursions (e.g., snorkeling is offered in all three ports), the
couple researched the quality of the activity and ranked the excursion among the
available alternatives, with higher numbers indicating better quality. Thus, snorkeling in
Jamaica is better than in Cozumel, and snorkeling in Cozumel is better than in Grand
Cayman. For the unique experiences, i.e., the turtle farm, the default rating was the a 3.
(Note - data used in this test question should not be construed as vacation advice.)
The vacationing management scientist sat down at his computer keyboard, cracked his
knuckles and decided on the scheme of location (J, C, or G) and excursion (S, P, H, L, Te
or Tu), for his decision variables. He wrote constraints that read:
JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu ≤ 3
JS + JP + JH + JL ≤ 1
CS + CP + CH + CL + CTe≤1
GS + GP + GH + GL + GTu ≤ 1
What do these constraints accomplish in the model and which ones are necessary?
________ error is the sum of the forecast errors.
In a transportation tableau with m rows and n columns, if there are fewer than n+m-1
allocations, the tableau is said to be ________.
Lenny, a graduate research assistant "moonlights" at the short order counter in the
student union snack bar in the evenings. He is the only one on duty at the counter
during the hours he works. Arrivals to the counter seem to follow the Poisson
distribution with a mean of 8 per hour. Each customer is served one at a time and the
service time follows an exponential distribution with a mean of 5 minutes.
The manager thinks that students will go elsewhere for lunch if they have to wait more
than 5 minutes. Therefore he's thinking of hiring another server to help Lenny, reducing
the customer service time to 4 minutes. How long will students wait in line if Lenny
gets help?
Compute the expected value of perfect information assuming that the probability of S2
is equal to 0.4.
Given the following data on the number of pints of ice cream sold at a local ice cream
store for a 6-period time frame:
Compute a 3-period moving average for period 6.
An office manager uses 400 boxes of file folders per year. The price is $8.50 per box for
an order size of 199 boxes or less, $8.00 per box for orders of 200 to 799 boxes, and
$7.50 per box for an order of 800 or more boxes. Carrying cost is 20 percent of the
price of the product and ordering costs are $80. What order quantity minimizes total
annual cost?
Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3
per gallon on its water-base paint. Both paints contain two ingredients, A and B. The
oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint
contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of
ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at
this time. The company wishes to use linear programming to determine the appropriate
mix of oil-base and water-base paint to produce to maximize its total profit. How much
oil-based and water-based paint should the Quickbrush make?
The probability of ending up in a state in the future is ________ of the starting state.
If the objective function is parallel to a constraint, the linear program could have
________.
What is the full set of constraints if the following situations occur? The Eiffel Tower
visit needed to take place at the same time has the half day at the Louvre. Students
taking the Paris Sewer tour had to wear the special sanitary beret available only from
the Bon Beret tour. Saba applies for university travel funds and supplements the
students' accounts with an extra $30 each.
A novice business analyst develops the following model to determine the optimal
combination of socks and underwear to take on his next business trip. The model is as
follows:
Maximize 5S+7U
subject to:
3S - 2U≤ 45
7S + 3U≤ 33
2S + 8U≤ 70
Solve this problem graphically and determine how many of each item the analyst
should pack.
A croissant shop produces two products: bear claws (B) and almond-filled croissants
(C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS (tablespoons)
of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast,
and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of
yeast, and 4800 TS of almond paste available for today's production run. The shop must
produce at least 400 almond-filled croissants due to customer demand. Bear claw
profits are 20 cents each, and almond-filled croissant profits are 30 cents each.
What is the formulation for this problem?
The XYZ manufacturing company produces ball bearings. The annual fixed cost is
$20,000 and the variable cost per ball bearing is $3. The price is related to demand
according to the following equation: 1000 - 8p.
What is the derivative of the profit function for the XYZ company? Simplify the terms
as much as possible.
The Cruise
Their cruise would port out of New Orleans and promised seven days with a panoply of
excursions in Jamaica, Cozumel, and Grand Cayman. A list of excursions at each site
and key features of each appear in the table. The excursions were all day affairs, so it
was possible to engage in only one per port. The cruise ship sailed at night and docked
at each of these three ports at the crack of dawn. By dinner time, the ship was on its
way to the next port and next set of excursions. The couple was energetic and active for
a pair of 52 year-olds., and while enjoying an upper middle class lifestyle, they didn't
want to spend money on excursions that might be better spent on tacky souvenirs. The
couple therefore budgeted $250 for the excursions the prices shown are per couple, so
for example, the $60 will pay for both of them to fill up on jerk chicken and mannish
water.
For each of the duplicate excursions (e.g., snorkeling is offered in all three ports), the
couple researched the quality of the activity and ranked the excursion among the
available alternatives, with higher numbers indicating better quality. Thus, snorkeling in
Jamaica is better than in Cozumel, and snorkeling in Cozumel is better than in Grand
Cayman. For the unique experiences, i.e., the turtle farm, the default rating was the a 3.
(Note - data used in this test question should not be construed as vacation advice.)
What is an appropriate objective function and constraints for this vacation?
If f(x) = 2x, what is the equation for generating x, given the random number r?
