1. Question:Acompanymakestwoproductsfromsteel; onerequires 2tonsofsteelandtheotherrequires3tons.Thereare100tonsofsteelavailabledaily.Aconstraintondaily production could bewrittenas:2x1+3x2≤100.
2. Question:Letx1,x2,andx3be0-1variableswhosevaluesindicatewhethertheprojectsarenotdone(0)oraredone(1)...
1. A company makes two products from steel; one requires 2 tons of steel and the other requires 3 tons. There
are 100 tons of steel available daily. A constraint on daily production could be written as: 2x1 + 3x2 ≤ 100.
True
False
2. Let x1 , x2 , and x3 be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done
(1). Which answer below indicates that at least two of the projects must be done?
3. The constraint x1 + x2 + x3 + x4 ≤ 2 means that two out of the first four projects must be selected.
True
False
4. Each point on the efficient frontier graph associated with the Markowitz portfolio model is
the minimum possible risk for the given return.
maximum return for the least risk.
maximum possible risk for the given return.
minimum diversification for the least risk.
5. Consider a maximal flow problem in which vehicle traffic entering a city is routed among several routes
before eventually leaving the city. When represented with a network,
None of the alternatives is
correct. the arcs represent one
way streets. the nodes represent
stoplights.
the nodes represent locations where speed limits change.
6. Assuming W1, W2 and W3 are 0 -1 integer variables, the constraint W1 + W2 + W3 < 1 is often called a
multiple-choice constraint.
k out of n alternatives constraint.
mutually exclusive constraint.
corequisite constraint.
, 7. Let M be the number of units to make and B be the number of units to buy. If it costs $2 to make a unit and $3
to buy a unit and 4000 units are needed, the objective function is
Max 2M + 3B
Min 4000 (M + B)
Max 8000M + 12000B
Min 2M + 3B
8. The dual price for a constraint that compares funds used with funds available is .058. This means that
the cost of additional funds is 5.8%.
no more funds are needed.
the objective was to minimize.
if more funds can be obtained at a rate of 5.5%, some should be.
9. Problem 9-11 (Algorithmic)
Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers
have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge
different prices for the components. Component price data (in price per unit) are as follows:
Supplier
Component 1 2 3
1 $12 $14 $15
2 $11 $10 $10
Each supplier has a limited capacity in terms of the total number of components it can supply.
However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity
to component 1, component 2, or any combination of the two components, if the total number of units
ordered is within its capacity. Supplier capacities are as follows:
Supplier 123
Capacity 550 950 800
If the Edwards production plan for the next period includes 1025 units of component 1 and 825 units of
component 2, what purchases do you recommend? That is, how many units of each component should be
ordered from each supplier?
10. To develop a portfolio that provides the best return possible with a minimum risk, the linear programming
model will have an objective function which
minimizes total risk.
maximizes the minimum return.
minimizes the maximum risk.
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