I have 3 sample questions I cannot figured out.  Can you please assist
me by showing me how to resolved these problems with detailed
breakdown, so I can have a good understanding on how these problems
were solved?  Can you please help?  I need it right away today by no
later than 3:00 P.M. (Pacific Standard Time), sorry for the rush. 
Thank You.  Here are the problems:

(1) The employee credit union at State University is planning the
allocation of funds for the coming year.  The credit union makes four
types of loans to its members.  In addition, the credit union invests
in risk-free securities to stabilize income.  The various
revenue-producing investments together with annual rates of return are
as follows:

Type of Loan/Investment	Annual Rate of Return (%)
Automobile loans	 8
Furniture loans	        10
Other secured loans	11
Signature loans	        12
Risk-free securities	 9

The credit union will have $2,000,000 available for investment during
the coming year.  State laws and credit union policies impose the
following restrictions on the composition of the loans and
investments.

ˇRisk-free securities may not exceed 30% of the total funds available
for investment.
ˇSignature loans may not exceed 10% of the funds invested in all loans
(automobile, furniture, other secured, and signature loans).
ˇFurniture laons plus other secured loans may not exceed the automobile loans.
ˇOther secured loans plus signature loans may not exceed the funds
invested in risk-free securities.

How should the $2,000,000 be allocated to each of the loan/investment
alternatives to maximize total annual return?  What is the projected
total annual return?
 
(2) The Ferguson Paper Company produces rolls of paper for use in
adding machines, desk calculators, and cash registers.  The rolls,
which are 200 feet long, are produced in widths of 1 ˝, 2 ˝, and 3 ˝
inches.  The production process provides 200-foot rolls in 10-inch
widths only.  The firm must therefore cut the rolls to the desired
final product sizes.  The seven cutting alternatives and the amount of
waste generated by each are as follows.

Cutting Alternatives	Number of Rolls	             Waste (inches)
	                1 ˝ in.	 2 ˝ in.  3 ˝ in.	
1	                6	 0	  0	     1
2	                0	 4	  0	     0
3	                2	 0	  2	     0
4	                0	 1	  2	     ˝
5	                1	 3	  0	     1
6	                1	 2	  1	     0
7	                4	 0	  1	     ˝

The minimum requirements for the three products are
Roll Width (inches)	1 ˝	2 ˝	3 ˝
Units	               1000	2000	4000

a. If the company wants to minimize the number of 10-inch rolls that
must be manufactured, how many 10-inch rolls will be processed on each
cutting alternative?  How many rolls are required, and what is the
total waste (inches)?

b. If the company wants to minimize the waste generated, how many
10-inch units will be processed on each cutting alternative?  How many
rolls are required, and what is the total waste (inches)?

c. What are the differences in approaches (a) and (b) to this problem?
 In this case, which objective do you prefer?  Explain.  What types of
situations would make the other objective more desirable?
 
(3) Frandec Company manufactures, assembles, and rebuilds material
handling equipment used in warehouses and distribution centers.  One
product, called a Liftmaster, is assembled from four components: a
frame, a motor, two supports, and a metal strap.  Frandec?s production
schedule calls for 5000 Liftmasters to be made next month.  Frandec
purchases the motors from an outside supplier, but the frames,
supports, and straps may either be manufactured by the company or
purchased from an outside supplier.  Manufacturing and purchase costs
per unit are shown.

Component	Manufacturing Cost	Purchase Cost
Frame	               $38.00	        $51.00
Support	               $11.50	        $15.00
Strap	               $ 6.50	        $ 7.50

Three departments are involved in the production of these components. 
The time (in minutes per unit) required to process each component in
each department and the available capacity (in hours) for the three
departments are as follows.

Component	Cutting	Department     Milling	    Shaping
Frame	              3.5	         2.2	      3.1
Support	              1.3	         1.7	      2.6
Strap	              0.8	          -	      1.7
Capacity (hours)      350	         420	      680

a. Formulate and solve a linear programming model for this make-or-buy
application.  How many of each component should be manufactured and
how many should be purchased?

b. What is the total cost of the manufacturing and purchasing plan?

c. How many hours of production time are used in each department?

d. How much should Frandec be willing to pay for an additional hour of
time in the shaping department?

e. Another manufacturer has offered to sell frames to Frandec for $45
each.  Could Frandec improve its position by pursuing this
opportunity?  Why or why not?

Thank You.