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there are 4 Lp problems solve it in spreadsheet using solver
1- A trust officer at the blackburg National Bank needss to determine how to invest $100,000 in the following collection of bonds to maximize the annual return.
Bond Annual Return Maturity Risk Tax-free
A 9.5% Long High Yes
B 8.0% Short Low Yes
C 9.0% Long Low No
D 9.0% Long High Yes
E 9.0% Short High No
The officer wants to invest at least 50% of the money in short -term issues and no more than 50% in high-risk issues. At least 30% of the founds should go in tax-free investment, and at least 40% of the total annual return should be tax free.
a. Formulate an LP model for this problem,
b. Create a spreadsheet model for this problem, and solve it using solver.
c. What is the optimal solution?
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2-The weedwacker 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 15000 gas trimmers. However, Weedwacker’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:
Hours Required per Trimmer
Electric Gas Hours Available
Production 0.20 0.40 10,000
Assembly 0.30 0.50 15,000
Packaging 0.10 0.10 5000
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. How many gas and electric trimmers should Weedwacker make, and how many should it buy from its competitor in order to fulfill its contract in the least costly manner?
a. Formulate an LP model for this problem,
b. Create a spreadsheet model for this problem, and solve it using solver.
c. What is the optimal solution?
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3- The Rent –A-Dent car rental company allows its customers to pick up a rental car at one location and return it to any of its locations. Currently, two locations (1 and 2) have 16 and 18 surplus cars, respectively, and four locations (3,4,5, and 6) each need 10 cars . The costs of getting the surplus cars from locations 1 and 2 to other locations are summarized in the following table.
Cost of Transporting cars between locations
Location 3 location 4 location5 location 6
Location 1 $54 $17 $23 $30
Location 2 $24 $18 $19 $31
Because 34 surplus cars are available at locations 1 and 2 , and 40 cars are needed at locations 3,4,5, and 6 , some locations will not receive as many cars as they need . However , management wants to make sure that all the surplus cars are sent where they are needed and that each location needing cars receives at least five.
a. Formulate an LP model for this problem,
b. Create a spreadsheet model for this problem, and solve it using solver.
c. What is the optimal solution?
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4- Incline Electronics produces three different products in a plant that is open 40 hours per week. Each product requires the following processing times (in hours) on each of three machines.
Product 1 product 2 product 3
Machine 1 2 2 1
Machine 2 3 4 6
Machine 3 4 6 5
Each machine must be run by one of 19 cross-trained workers who are each available 35 hours per week. The plant has 10 type 1 machines available, 6 type 2 machines available , and 8 type 3 machines available . Products 1,2, and 3 contribute $90,$120,and $150,respectively, in marginal profit per unit produced.
a. Formulate an LP model for this problem,
b. Implement your model in a spreadsheet and solve it .
c. What is the optimal solution?
d. How many workers should be assigned to each type of machine?
