UNLV Linear Programs and Graphical Approach on Lp Problem Equations Math Questions

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Can you help me do these 5 questions of math for me?You can only insert answers next to the equations.You do not have to write the processes how you solved them

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Problem Set 5
1. A bank has $850,000 in assets to allocate among investments in bonds, home mortgages, car
loans, and personal loans. Bonds are expected to produce a return of 10%, mortgages 8.5%,
car loans 9.5%, and personal loans 12.5% To make sure the portfolio is not too risky, the
bank wants to restrict personal loans to no more than 30% of the total portfolio. The bank
also wants to ensure that more money is invested in mortgages than in personal loans. It also
wants to invest more in bonds than in personal loans.
a. Write out the linear program
2. The ELC Corporation manufactures two industrial-sized electrical devices: generators and
alternators. Both of these products require wiring and testing during the assembly process.
Each generator requires 4 hours of wiring and 2 hour of testing and can be sold for a $450
profit. Each alternator requires 6 hours of wiring and 1 hours of testing and can be sold for a
$200 profit. There are 260 hours of wiring time and 140 hours of testing time available in the
next production period and ELC wants to maximize profit.
a. Write out the linear program
b. Use the graphical approach to solve this LP problem.
3. Black Ridge Refining extracts minerals from ore mined at two different sites in Utah. Each
ton of ore type 1 contains 15% copper, 20% zinc and 15% magnesium. Each ton of ore type 2
contains 25% copper, 25% zinc and 10% magnesium. Ore type 1 costs $90 per ton and ore
type 2 costs $120 per ton. Black Ridge would like to buy enough ore to extract at least 8 tons
of copper, 6 tons of zinc, and 5 tons of magnesium in the least costly manner.
a. Write out the linear program
b. Use the graphical approach to solve this LP problem.
4. A bank has $850,000 in assets to allocate among investments in bonds, home mortgages, car
loans, and personal loans. Bonds are expected to produce a return of 10%, mortgages 8.5%,
car loans 9.5%, and personal loans 12.5% To make sure the portfolio is not too risky, the
bank wants to restrict personal loans to no more than 30% of the total portfolio. The bank
also wants to ensure that more money is invested in mortgages than in personal loans. It also
wants to invest more in bonds than in personal loans.
Having written out an LP model for this problem with the objective of maximizing the
expected return on the portfolio in the last assignment; Find the solution with Solver.
5. The Wacker Company manufactures two types of lawn trimmers: an electric model and a gas
model. The company has contracted to supply a national discount retail chain with a total of
30,000 electric trimmers and 15,000 gas trimmers. However, Wacker’s production capability
is limited in three departments: production, assembly, and packaging. The following table
summarizes the hours of processing time available and the processing time required by each
department, for both types of trimmers:
Production
Assembly
Packaging
Hours Required per Trimmer
Electric
Gas
Hours Available
0.20
0.40
10,000
0.30
0.50
15,000
0.10
0.10
5,000
The company makes its electric trimmer in-house for $55 and its gas trimmer for $85.
Alternatively, it can buy electric and gas trimmers from another source for $67 and $95,
respectively.
a. Develop a spreadsheet model to determine how many gas and electric trimmers
the company should make and how many it should buy to fulfill its contract in the
least costly manner.
Use a Sensitivity Report to answer the following:
b. If the cost to make gas trimmers increased to $90 per unit, how would the optimal
solution change? Explain.
c. How much should the company be willing to pay to acquire additional capacity in
the assembly area? Explain.
d. How much should the company be willing to pay to acquire additional capacity in
the production area? Explain.
e. What will happen to total cost if the demand for electric trimmers increases by
1,000? Explain.

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Tags:
Linear Program

Personal Loans

home mortgages

graphical approach

least cost

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