The PENTEL Corporation manufactures three different types of computer chips

The PENTEL Corporation manufactures three different types of computer chips. Each type of chip requires different amounts of processing time in three different departments as summarized in the following table.

Processing Hours Required per 100 Chips              Hours Available

Chip A   Chip B   Chip C

Dept 1   3              2              4              10,000

Dept 2   2              4              3              9,000

Dept 3   3              4              2              11,000

The total profit (in dollars) for each type of chip may be described as follows:

Chip A profit

= −0.36A2 + 8.29A + 540

Chip B profit

= −0.59B2 + 9.46B + 1,108

Chip C profit

= −0.48C2 + 11.00C + 850

where A, B, and C represent the number of chips produced in 100s.

(a)

Formulate an NLP model for this problem to maximize profit (in dollars).

MAX:    

Subject to:

department 1   

department 2   

department 3   

A, B, C, ≥ 0

(b)

Implement your model in a spreadsheet and solve it. What is the optimal solution? (Round your numerical values to two decimal places.)

(A, B, C) =

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RAGSMDA9 8.E.014.

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Suppose a gift shop in Myrtle Beach has an annual demand for 14,000 units for a souvenir kitchen magnet that it buys for $0.40 per unit. Assume it costs $12 to place an order and the inventory carrying cost is 23% of the item's unit cost. Use Solver to determine the optimal order quantity if the company wants to minimize the total cost of procuring this item. (Suppose the gift shop currently makes orders quarterly. Set the convergence value for the Standard GRG Nonlinear Engine to at most 0.0000001.)

(a)

What is the optimal order quantity? (Round your answer to the nearest integer.)

(b)

What is the total cost (in dollars) associated with this order quantity? (Round your answer to two decimal places.)

$

(c)

What is the annual order cost (in dollars) for this solution? (Round your answer to two decimal places.)

$

What is the annual inventory holding cost (in dollars) for this solution? (Round your answer to two decimal places.)

$

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3.

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RAGSMDA9 8.E.028.

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An air-ambulance service in Colorado is interested in keeping its helicopter in a central location that would minimize the flight distance to four major ski resorts. An X-Y grid was laid over a map of the area to determine the following latitude and longitude coordinates for the four resorts:

Resort   Longitude            Latitude

Bumpyride          36           58

Keyrock                45           47

Asprin   36           92

Goldenrod          21           66

(a)

Formulate an NLP model to determine where the ambulance service should be located in order to minimize the total distance to each resort. (Let X be the longitude of the ambulance service location and Y be the latitude.)

MIN:     

Subject to:

X, Y ≥ 0

(b)

Implement your model in a spreadsheet and solve it. Where should the ambulance service be located? (Set the convergence value for the Standard GRG Nonlinear Engine to at most 0.0000001. Round your numerical values to one decimal place.)

(X, Y) =

(c)

How might you incorporate the following factors into your model?

the average number of skiers and accidents at the different resorts

Two more objective functions could be incorporated into the model which give the number of skiers/accidents averaged across all four resorts in terms of X and Y. Then, the problem would become a multiple objective optimization problem with appropriate weights assigned to the three objective functions.

Weights could be assigned to the distances in the objective function to reflect the differences in the numbers of skiers/accidents at different resorts.   

Constraints could be added to keep the number of skiers/accidents in the optimal solution below a certain threshold at each resort.

The number of skiers/accidents could be accounted for by calculating the distances to each resort using more complex nonlinear functions in the objective function.

the topography of the area

To ensure the ambulance has to cross as little difficult terrain as possible, constraints could be added to keep the maximum travel time from the ambulance service to each resort below a certain threshold.

The topography of the area could be accounted for by calculating the distances to each resort using more complex nonlinear functions in the objective function.   

To ensure the ambulance has to cross as little difficult terrain as possible, constraints could be added to keep the maximum distance from the ambulance service to each resort below a certain threshold.

Weights could be assigned to the distances in the objective function to reflect the complex differences in topography while traveling to each resort.

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RAGSMDA9 8.E.033.

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An investor wants to determine the safest way to structure a portfolio from several investments. Investment A produces an average annual return of 14% with a variance of 0.025. Investment B produces an average rate of return of 9% with a variance of 0.015. Investment C produces an average rate of return of 8% with a variance of 0.010. Investments A and B have a covariance of 0.00029, and investments A and C have a covariance of

−0.005.

 Investments B and C have a covariance of 0.00135. (Let pA, pB, and pC be the proportion of total funds invested in investments A, B, and C, respectively.)

(a)

Suppose the investor wants to achieve at least a 12% return. What is the least risky way of achieving this goal? (Round your numeric values to three decimal places.)

(pA, pB, pC) =

(b)

Suppose the investor regards risk minimization as being five times more important than maximizing return. What portfolio would be most appropriate for the investor? (Round your numeric values to three decimal places.)

(pA, pB, pC) =