Optimal solution | Business & Finance homework help

FINAL EXAM

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fall 2014 –  BSC 400

 

instructor: M.Schmidtova

120 minutes, no books/no notes, only calculators are allowed

normal table.jpg

 

 

Expected time of activity =         Variance       

 

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Name:

 

Score: 60/

 

 

 

 

1.        Suppose the following LPP: 7x2pts=14pts]

A furniture manufacturer makes two types of coffee tables. A circular table (X) requires 3h of skilled labor and 6h of unskilled labor and produces a profit of $50. A rectangular table (Y) requires 2h of each type of labor and yields a profit of $30. If 90h of skilled labor and 120h of unskilled labor are available for a week, determine how many of each type of table should be made in order to maximize the profit.

The task was formulated in this way: 

          

                                                                                                           

 

The MS output is as follows:

 

a)      What is the optimal solution? What are values of both variables that produce the optimized solution? What is value of optimized profit?

 

 

 

 

b)      Considering the type of constraint, do the constraints deal with slack or surplus variable? What is the meaning of its zero value?

 

 

 

c)      Will the optimal solution change if the objective function is changed to P=60X +30Y? Explain.

 

 

 

 

 

 

 

 

 

d)     Will the optimal solution change if the objective function is changed to P= 48X +33Y ? Explain.

 

 

 

 

 

 

 

 

 

e)      Will the optimal solution change if the second constraint is changed to 6S + 2Y 200 ? Explain.

 

 

 

 

 

 

 

 

 

f)       Will the optimal solution change if constants on the right sides of constraints are changed to 75, 95, respectively? Explain.

 

 

 

 

 

 

 

 

 

g)      Interpret the dual price of 13.333 clearly. What will be new value of Profit function?

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. Only formulate the problem: [5+5=10pts]

a)      You have up to $12,000 to invest, and three different funds from which to choose. The municipal bond fund has a 7% return, the local bank’s CDs have an 8% return, and the high-risk account has an expected (hoped-for) 12% return. To minimize risk, you decide not to invest any more than $2,000 in the high-risk account. For tax reasons, you need to invest at least three times as much in the municipal bonds as in the bank CDs. Assuming the year-end yields are as expected, what are the optimal investment amounts?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b)      The Buds-R-Us Florist has to order roses and carnations for Valentine’s Day.  Roses cost the florist $20 per dozen and carnation cost $5 per dozen. The profit on roses is $20 per dozen and on carnations it is $8 per dozen. The florist can spend at most $450 on flowers and must order at least 20 dozen carnations, but the florist can order no more than 60 dozen flowers. How many of each kind should he order in order to maximize the profit?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.      A company is considering building a new complex. The project leader developed the following list of activities and immediate predecessors. Construct a project network for this problem. [4pts]

 

activity

A

B

C

D

E

F

G

H

Immediate predecessor

A,B

C

C

D,E

E

F,G

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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4.      The following network is given: [3+3+2=8pts]

 

a)      Find the expected project completion time. The data are given in weeks.

 

 

 

 

 

 

 

 

 

 

 

 

b)      Find the critical path.

 

 

 

 

 

 

 

 

 

 

c)      Select any activity with nonzero slack and interpret its slack value clearly.