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Billy Hill's Still
William J Hill runs a small batch artisnal bourbon distillery at a secluded location in the
hills of Kentucky. He makes two products, known among his customers as Rotgut and
White Lightning. The recipes for the two have been passed down in the Hill family for
generations and are Rotgut: 1 bushel of corn, 3 pounds of sugar, 2 hours of cooking
time. For the premium blend, White Lightning, he needs 2 bushels of corn, 2 pounds of
sugar, and 3 hours of cooking time. Both recipes make enough to fill two jugs, which
sell for $8 apiece for Rotgut and $12 apiece for White Lightning.
A quick inventory one crisp autumn morning reveals that William has on hand 40
bushels of corn, 70 pounds of sugar, and 50 jugs. He would like to brew up a few
artisnal batches, but has recently received a tip that certain agencies have taken an
interest in his talents and may be paying him a visit in three days, hence he plans to
restrict any brewing activity to 72 hours at most, before he retreats to his home away
from home, Lubbock.
William cleans his equipment, lights a fire, and ponders the objectives. Obviously the
first priority is restricting himself to 72 hours of work any more than that and he runs
the risk of an extended holiday. His second priority to make enough to acquire materials
for the next production run and fund his daughter's college tuition - he believes that
$500 would make this production run worth his while. His third and fourth priorities are
not to have too much perishable inventory, so he wants to make sure he doesn't have too
many bushels of corn on hand (third priority) nor does he want too many pounds of
sugar on hand (fourth priority).What is the profit constraint?
16R + 24W + d2
If price and demand are related by the function v = 15 + 15p and the fixed cost is $150
while the variable cost is $5, then the expression for profit is ________.
The ________ of a random variable is computed by multiplying each possible value of
the variable by its probability and summing these products.
Random numbers of a mathematical process instead of a physical process are ________
numbers.
In a transportation tableau to rectify a degenerate tableau, an empty cell must artificially
be treated as an ________ cell.
Comedy Pasture II
A horse and two llamas are discussing the key areas of their domain on a lazy summer
afternoon. The llamas favor the pond and shade and like to browse the fruit trees and
oaks on the property, making their way to the barn only when their owner favors them
with some oats. The horse prefers to graze the grass and hay for food and drink from the
pond but will race up to the barn when the owner is handing out oats up there. Between
the three of them, they have stepped off the distances between many of these key points
several times and believe that they have developed an accurate map, shown below. This
map shows the number of loads that can be hauled between all connected points on the
property. As incredible as it may seem, neither the horse nor the llamas have had any
training in management science, which is where you come in.
The llamas took pride in the centuries old use as pack animals in the South American
Andes. Using only their network of nodes, Fruit, Barn, Grass, Oak, Shade, Hay and
Pond, they figured they could easily outhaul the horse. Use the capacities indicated on
each of the branches to determine the maximal flow from the Barn down to the pond.
Given an EOQ model with shortages in which annual demand is 4200 units, Co = $160,
Cc = $7 per unit per year and CS = $25, what is the total annual shortage cost?
A bakery uses an average of 60 ounces of organic orange juice daily. Demand is
normally distributed with a standard deviation of 15 ounces. The bakery places orders
every seven days. The lead time for delivery of the juice is three days.
If the bakery has 190 ounces at the time an order is placed, how much should be
ordered?
If all the variables are held constant, the total inventory cost in a noninstantaneous
receipts model is ________ than the total cost in the basic EOQ model.
A manufacturer must decide whether to build a small or a large plant at a new location.
Demand at the location can be either low or high, with probabilities estimated to be 0.4
and 0.6, respectively. If a small plant is built, and demand is high, the production
manager may choose to maintain the current size or to expand. The net present value of
profits is $223,000 if the firm chooses not to expand. However, if the firm chooses to
expand, there is a 50% chance that the net present value of the returns will be 330,000
and a 50% chance the estimated net present value of profits will be $210,000. If a small
facility is built and demand is low, there is no reason to expand and the net present
value of the profits is $200,000. However, if a large facility is built and the demand
turns out to be low, the choice is to do nothing with a net present value of $40,000 or to
stimulate demand through local advertising. The response to advertising can be either
modest with a probability of .3 or favorable with a probability of .7. If the response to
advertising is modest, the net present value of the profits is $20,000. However, if the
response to advertising is favorable, then the net present value of the profits is
$220,000. Finally, if the large plant is built and the demand happens to be high, the net
present value of the profits $800,000.
Draw a decision tree and determine the payoff for each decision and event node. Which
alternative should the manufacturer choose?
The efficiency of sample information multiplied by the expected value of perfect
information is ________.
In setting up the an intermediate (transshipment) node constraint, assume that there are
three sources, two intermediate nodes, and two destinations, and travel is possible
between all sources and the intermediate nodes and between all intermediate nodes and
all destinations for a given transshipment problem. In addition, assume that no travel is
possible between source nodes, between intermediate nodes, and between destination
nodes, and no direct travel from source nodes to destination nodes. Let the source nodes
be labeled as 1, 2, 3, the intermediate nodes be labeled as 4 and 5, and the destination
nodes be labeled as 6 and 7.
If there are 175 units demanded at destination 6, state the constraint for destination 6.
The ________ reflects the approximate change in the objective function resulting from
a unit change in the quantity (right-hand-side) value of the constraint.
A production of 300 units of Twiddle Bugs, an educational toy for children, must be
completed within 1 week by BugU Manufacturing. Two production lines are available,
each for 30 hours during the week. Production line 1 can produce five units per hour
and production line 2 can produce four units an hour. Line 1 costs $50 per hour to
operate and line 2 costs $55 per hour. Overtime is available for line 1 at $15 per hour
and for line 2 at $12 per hour. Management goals in decreasing order are:
P1: Produce 300 units.
P2: Maximum allowable overtime of 6 hours for line 1.
P3: Cost of overtime must not exceed $750.
P4: Avoid the underutilization of either production line. Assign weights that are
proportional to their production capability.
P5: Producing more than 300 units is 1-1/2 times as undesirable as producing under 300
units.
What are the constraints for this problem?
P3: 50(x1 - 30) + 55(x2 - 30) + d2
- - d4
+=30
4P4Bd5
Given the following linear programming problem:
maximize 4x1 + 3x2
subject to 4x1 + 3x2 ≤23
5x1 - x2 ≤ 5
x1, x2 ≥ 0
What is the value of X1 in the final tableau?
A graduate research assistant "moonlights" at the short order counter in the student
union snack bar in the evenings. He is considering asking for help taking orders, but
needs to convince the management that they should hire another student. Because he is
taking a simulation class, he thinks it may be the perfect way to convince management
to hire more help if he can show that customers have to wait a long time. When a
customer arrives, he takes their order and their payment, prepares the food, gives it to
the customer, and then takes the order from the next person in line. If someone arrives
while he's cooking an order, they have to wait until he's completed the current order. He
is working on the simulation and a portion is shown below.
Complete the table and determine the average customer waiting time and the utilization
of the cook.
Complete the table and determine the average customer waiting time and the utilization
of the cook.
Consider a capital budgeting example with five projects from which to select. Let x1 = 1
if project a is selected, 0 if not, for a = 1, 2, 3, 4, 5. Projects cost $100, $200, $150, $75,
and $300, respectively. The budget is $450.
Write the appropriate constraint for the following condition: If project 1 is chosen,
project 5 must not be chosen.
________ in linear programming is when a basic variable takes on a value of zero (i.e.,
a zero in the right-hand side of the constraints of the tableau).
The Lagrangian function is differentiated with respect to each variable and the resulting
equations are solved ________ to obtain the value of each variable.
