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An investor has $80,000 to invest in three stocks, stock A costs $100, stock B costs
$120 and stock C costs $80. Each stock A has a risk factor of 8, each stock B has a risk
factor of 10 and each stock C has a risk factor of 7. The investor believes that the sum
of the risk factors for all stocks purchase should not exceed 6000. The projected annual
growth rate for the three stocks are 9%, 13% and 8% respectively. The projected annual
dividend income from these stocks are as follows: Stock A: $14/stock, Stock B:
$15/stock, and Stock C: $20/stock. The investor desires an annual dividend income of
$10,000. The investor has established the following goals in order of their importance:
(1) The investor believes that the budget cannot be exceeded. (d1)(2) The risk factor
should not exceed the target amount of 6000. (d2)(3) The average annual growth rate in
stock prices must be at least 10%. (d3)(4) The investor desires a dividend income of at
least $10,000. (d4)
Write the budget constraint
________ are numbers equally likely to be chosen from a large population of numbers.
A graphical representation of a linear program is shown below. The shaded area
represents the feasible region, and the dashed line in the middle is the slope of the
objective function.
What would the be the new slope of the objective function if multiple optimal solutions
occurred along line segment AB?
Bullseye Shirt Company makes three types of shirts: athletic, varsity, and surfer. The
shirts are made from Different combinations of cotton and rayon. The cost per yard of
cotton is $5 and the cost for rayon is $7. Bullseye can receive up to 4000 yards of
cotton and 3000 yards of rayon per week.
The table below shows relevant manufacturing information:
Write the constraints for the fabric requirements.
The daily sales of a peanut butter at Power's Grocery are normally distributed, with a
mean of 12 jars and a standard deviation of 4. The manager checks the inventories on
shelves and places an order every three days. Delivery lead time is two days.
In a noninstantaneous receipt model, daily demand is 55 units and daily production is
120 units, Co = $70 and Cc = $4 per unit/year. The production facility operates 300 days
per year. What is the optimal order quantity?
Administrators at a university are planning to offer a summer seminar. It costs $3000 to
reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per
student for the administrators to provide the course materials. If we know that 20 people
will attend, what price should be charged per person to break even?
A Markov process has the following transition matrix:
A B
A 0.65 0.35
B 0.45 0.55
What are the steady state probabilities?
In the basic EOQ model, as the size of the order increases, the annual ________ cost
decreases.
A courier service located at the south edge of downtown dispatches three bicycle
couriers with identical sets of architectural renderings that must go to three
XOAXOAerent downtown law offices as quickly as possible. This problem is a likely
candidate for analysis using ________.
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.
The production manager for Beer etc. produces two kinds of beer: light and dark. Two
of his resources are constrained: malt, of which he can get at most 4800 oz per week;
and wheat, of which he can get at most 3200 oz per week. Each bottle of light beer
requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt
and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are
$1 per bottle. What are the optimal weekly profits?
In the method of ________, constraints as multiples of multiplier λ are subtracted from
the objective function, which is then diferentiated with respect to each variable and
solved.
A(n) ________ measures the degree of inconsistency in pairwise comparisons.
________ is a gradual, long-term, upward or downward movement of demand.
In a media selection problem, instead of having an objective of maximizing profit or
minimizing cost, generally the objective is to maximize the ________.
If the number of sources is greater than the number of destinations, then we have a(n)
________ assignment problem.
