# Systems Analysis and Design Evaluation

In 1–3 paragraphs for each question, answer the questions referred to in your reading assignment for this Unit.

Chapter 7: Alternatives and Models in Decision Making

· Question 1: The following table shows five opportunities to make a profit under three possible scenarios of the future. Select the best alternative based on the most probable future criterion.

 Probability 0.3 F1 (\$M = million) 0.2 F2 (\$M = million) 0.5 F3 (\$M = million) Alternative 1 2 M 2 M 7.6 M Alternative 2 -4 M 3.2 M 10.8 M Alternative 3 0 3.6 M 10 M Alternative 4 2.2 M 5.6 M 4 M Alternative 5 8 M 1.8 M 3.6 M

· Question 2: The following table shows the payoffs in measures of utility (in utiles) for three alternatives and three states of nature.

 State of Nature S1 S2 S3 A1 100 160 160 A2 120 140 40 A3 180 60 120

Chapter 8: Models for Economic Evaluation

· Question 1: You are financing a new car with a three-year loan at 10.5% annual nominal interest, compounded monthly. The price of the car is \$14,500. Your down payment is \$1,500. What are your monthly payments at 10.5%? (Assume your payments start one month after the purchase, or at the end of the first period.)

· Question 2: You decide that the maximum monthly home mortgage payment that you can afford is \$930.00. You can make a \$12,000 down payment, and annual interest rates are currently 7.5%. If you obtain a 30-year mortgage, what is the maximum purchase price that you can afford?

· Question 3: You have obtained a 25-year, \$172,500 home mortgage at 8.8% annual interest. You anticipate that you will own the house for four years and then sell it, repaying the loan with a balloon payment. What will your balloon payment be?

· Question 4: If you deposit \$2,000 in a savings account that pays 7.2% annual interest compounded annually and make no other deposits to the account, how long will it take for the account to grow to \$3,000.

· Question 5: You opened an individual retirement account (IRA) on April 14, 2005 with, a deposit of \$2,000. \$80.00 is deducted from your paycheck, and you are paid twice a month The account pays 6.3% annual interest compounded semimonthly. How much will be in the account on April 14, 2020?

· Question 6: For each of the following investments, what is the accumulated amount?

· \$16,000 at 7.2% compounded annually over 5 years.

· \$100,000 at 10% compounded annually over 10 years.

· Question 7: Given a year-end series of receipts with the first year of \$2,000 and increasing by 6% per year to year 20 with an interest rate of 6%, what is the present value?

· Question 8: There are two available design alternatives for a system. Each system has an expected future of this life cycle cost. The following table gives the costs for the corresponding three futures (in millions of dollars). The probability for the optimistic future is 30%, expected future is 50%, and a pessimistic future of 20%. Use an interest rate of 10% to select the best alternative.

 Design I Years Futures 1 2 3 4 5 6 7 8 9 10 11 12 Optimistic 0.8 1.2 10 14 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 Expected 1.2 1.6 2.0 10.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 Pessimistic 1.6 1.8 2.0 14.0 10.0 2.4 2.4 2.4 2.4 2.4 2.4 2.4

 Design II Years Futures 1 2 3 4 5 6 7 8 9 10 11 12 Optimistic 0.8 0.8 0.8 2.0 6.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 Expected 1.2 1.6 2.0 6.0 12.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 Pessimistic 1.2 1.6 2.0 10.0 12.0 3.1 6.2 6.2 6.2 6.2 6.2 6.2

· Question 9: Using Question 3 of Chapter 8, prepare a decision evaluation matrix. Choose the best alternative based on the following decision rules or criteria: Laplace, maximax, maximin, and Hurwicz with a = 0.6. Also, assume that the choice is under uncertainty.

· Question 10: It is estimated the annual sales of a new product will be 3,000 the first year, increasing sales by 1,000 per year until 6,000 units are sold in the fourth year. Proposal A purchased equipment at \$13,000 with a salvage value of \$3,000 at the end of 4 years. Proposal B purchased equipment costing \$30,000 with a salvage value of \$6,000 at the end of 4 years. Proposal A has a variable cost per unit of \$0.75, while Proposal B has a variable cost per unit of \$0.25. Assuming an interest rate of 9%, which proposal is acceptable for the four-year production period?

· Question 11: Two plants producing the same product are owned by a manufacturing company. Plant A has a capacity of 120,000 units, while plant B has 160,000 units of capacity. The annual cost is fixed for both plants where plant A is \$520,000 per year and plant B is \$560,000. The variable cost for plant A is \$6.40 per unit, and the variable cost for plant B is \$7.80 per unit. Plant A is operating at 35% capacity, and plant B is operating at 40% capacity.

· Determine the following costs for both plants:

· Total costs of production

· Total cost and average cost of total output

· Total cost to company and cost per unit if all production comes from plant A

· Total cost to company and cost per unit if all production comes from plant B

Chapter 9: Classical Optimization Theory

· Question 1: Assume that you want to decide between alternate ways of spending an eight-hour day; that is, you want to allocate your resource time. Assume you find it five times more fun to play pool in the lounge than to work, but you also feel that you should work at least three times as many hours as you play pool. The decision problem is how many hours to play and how many to work to maximize your objective—fun.

· Question 2: A man operates a pushcart. He sells hot dogs and sodas. His car can support 210 pounds. A hot dog weighs 2 ounces, and a soda weighs 8 ounces. He knows from experience that he must have at least 60 sodas and at least 80 hot dogs. He also knows that for every two hot dogs he sells, he needs at least one soda. Given that he makes \$0.08 profit on a hot dog and \$0.04 profit on a soda, find how many sodas and hot dogs he must have to maximize profits.

· Question 3: A small plant makes two types of automobile parts. It buys castings that are machined, bored, and polished. The data shown in Table 1 are given. Castings for Part A cost \$2 each; for Part B, they cost \$3 each. They sell for \$5 and \$6, respectfully. The three machines have running costs of \$20, \$14, and \$17.50 per hour. Assuming that any combination of Parts A and B can be sold, what product mix maximizes the profit?

 Part A Part B Capacity Machining Capacity 25/hr 40/hr Boring Capacity 28/hr 35/hr Polishing Capacity 35/hr 25/hr

· Question 4: Graphically solve for the values of x and y that maximize the following function:

· Z = 4.4x + 7.6y

· Subject to the following constraints:

· 4.8x + 6.4y = 280

· 5.2y = 160

· 8.2x = 240

· x = 0

· y = 0

Your response should address each of the major points of each question:

· For each question, write a 3-paragraph answer.

· Each response should include at least 1 reference to text, and all sources should be cited in APA format.

· Grammar, spelling, punctuation, and format should be correct and professional.

For the questions that include problem solutions, use the following guidelines for your answers:

· The final solution should be correct.

· The analytical process for solving the problem should be neatly laid out, and it should be logically defined.

· The number of arithmetical errors will be considered.

Be sure to cite all references in APA format.