Building lego furniture linear programming answers

Dr. Kuei Self-assessment (draft) - (before) Midterm

Name:

In accordance with the Honor Code, I certify that my answers here are my own work

Be sure to read each question carefully, to ask for explanation if you do not understand a question (however, please don't ask your instructor about solution procedures/strategies) .

In total, there are two sections:

Part 1 (question) ( Total : 13 points )

Part 2 – (multiple choice - Total: 32 points)(2 Points Each)

Part 1 (Total:13 points) please don't ask your instructor about solution procedures/strategies

1. (8 points)

Big Hart Manufacturing makes three products. One of them is Star War Lego Product 001. The cost of producing the Star War Lego Product 001 includes a setup cost of $500,000 and a unit cost of $75 per unit produced.

The demand per year for the Star War Lego Product 001 is a function of its selling price (i.e. p). Marketing experts estimate that there is a demand for 20,000 units, if it were free, and that this demand shrinks by 80 units for every dollar in the price of the product. As a result, demand is a linear function, namely, Demand (D) or Volume (V) = 20,000-80*p. p is the price of Star War Lego Product 001.

Big Hart Manufacturing plans to sell Star War Lego Product 001 for $162. Build a spreadsheet model in Excel to calculate the profit/loss for a given demand.

Question 1 (2 points): Create an influence diagram.

Hint:

Your Answer: =____________________

Your Answer: =_____________________

Question 2 (1 point): Define the decision variable.

Your Answer: _____________________

Question 3 (5 points): Use a data table that varies price from $70 to $210 increment of $10 to find the price range that maximizes profit.

Hint:

Your Answer: _____________________

2. (5 points) The Byte computer company produces two models of computers, Plain and Fancy. It wants to plan how many computers to produce next month to maximize profits. Producing these computers requires wiring, assembly and inspection time. Each computer produces a certain level of profits but faces a limited demand. There are a limited number of wiring, assembly and inspection hours available next month. The data for this problem is summarized in the following table.

Computer

Profit per

Maximum

demand for

Wiring Hours

Assembly

Hours

Inspection

Hours

Model

Model ($)

product

Required

Required

Required

Plain

30

80

0.4

0.5

0.2

Fancy

40

90

0.5

0.4

0.3

Hours Available

50

50

22

Let X1 = Number of Plain computers produce

X2 = Number of Fancy computers to produce

Formulate the LP model for this problem.

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*** (After Final) Announcement***

Now that the grades are final I will NOT:

Change your grade once that is determined

Part 2 (you must answer all 16 questions in this section) (multiple choice - Total: 32 points)(2 Points Each)

please don't ask your instructor about solution procedures/strategies

______1. What does the Excel "=SUMPRODUCT(A1:A5,C6;C10)" function do?

a. Sums each range and multiplies the sums.

b. Sum each pair of cells and multiples each sum.

c. Multiplies the contents of cells containing the =SUM() command.

d. Multiplies each pair of cells in two arrays matched by position and sums the products.

______2. Which of the following analytical techniques helps us arrive at the best decision (i.e. determine the best ways to operate and balance all constraints)?

a. Predictive analytics

b. Data mining

c. Prescriptive analytics

d. Descriptive analytics

_______3. Which of the following gives the proportion of items in each bin?

a. Frequency

b. Percent frequency

c. Relative frequency

d. Bin proportion

_____4. For data having a bell-shaped distribution (i.e. Normal distribution), approximately _____ percent of the data values will be within one standard deviation of the mean.

a. 95

b. 66

c. 68

d. 97

____5. Any data value with a z-score less than –3 or greater than +3 is treated as a(n)

a. Outlier (i.e. defective item).

b. usual value.

c. Non-defective value.

d. z-score value.

______6. Camm Industries produces different types of raw materials and it is interested in using simulation to estimate the profit per unit for its new product X. The selling price for the product will be $40 per unit. Probability distributions for the raw material cost, the production cost, and the marketing cost are estimated as follows:

Raw Material Cost ($)

Probability

Production Cost ($)

Probability

Marketing Cost ($)

Probability

16

0.20

10

0.25

5

0.40

18

0.30

11

0.45

6

0.60

20

0.35

12

0.30

22

0.15

Compute profit per unit for the worst case.

a. 0

b. 3

c. 5

d. 9

e. None of the above

______7. The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits.

X1 = number of product 1 produced in each batch

X2 = number of product 2 produced in each batch

MAX: 150 X1 + 250 X2

Subject to: 2 X1 + 5 X2 ≤ 200 − resource 1

3 X1 + 7 X2 ≤ 175 − resource 2

X1, X2 ≥ 0

How many units of resource 2 are consumed by each unit of product 1 produced?

a. 1

b. 2

c. 3

d. 5

The following business story pertains to questions 8 to 9

Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.

Let X1 = Number of Beds to produce

X2 = Number of Desks to produce

The LP model for the problem is

MAX: 30 X1 + 40 X2

Subject to: 6 X1 + 4 X2 ≤ 36 (carpentry)

4 X1 + 8 X2 ≤ 40 (varnishing)

X2 ≤ 8 (demand for desks)

X1, X2 ≥ 0

Exhibit 1
A

B

C

D

E

Jones Furniture

Beds

Desks

Number to make:

0

0

Total Profit:

Unit profit:

30

40

Constraints:

Used

Available

Carpentry

6

4

36

Varnishing

4

8

40

Desk demand

1

8

_____8. Refer to Exhibit 1. Which of the following statements represent the carpentry, varnishing and limited demand for desks constraints?

a. B4:C4 ≤ B5:C5

b. E5 ≤ 0

c. D8:D10 ≤ E8:E10

d. E8:E10 ≤ D8:D10

______9. Refer to Exhibit 1. What formula should be entered in cell E5 (i.e. objective function) in the accompanying Excel spreadsheet to compute total profit?

a. =B4*B5+C4*C5

b. =SUMPRODUCT(B8:C8,$B$4:$C$4)

c. =SUM(B5:C5)

d. =SUM(E8:E10)

______10. A manager is simulating the number of times a machine operator stops a machine to make adjustments. After careful study the manager found that the number of stops ranged from one to four per cycle and that each number of stops was equally likely. Using the random numbers 0.6380 and 0.8549 (in that order), the next two simulated cycles would respectively have stops for adjustment of: a. 2 and 2; b. 1 and 2; c. 4 and 3; d. 3 and 3; e. 3 and 4.; f. none of the above

_____11. Tim wishes to invest his inheritance of $100,000 so that his return on investment is maximized, but he also wishes to keep his risk level relatively low. He has decided to invest his money in any of three possible ways: CDS, which pay a guaranteed 8 percent; stocks, which have an expected return of 12 percent; and a money market mutual fund, which is expected to return 10 percent. In formulating this as a linear programming problem, Tim defines the variables as follows: C=dollars invested in CDs; S=dollars invested in stocks; M=dollars invested in money market mutual fund.

What would the objective function be? a) max 0.08C+0.12S+0.1M, b) max C+S+M, c) max 10000(0.08C+0.12S+0.1M), d) max 0.3C+0.3S+0.3M, e) none of the above.

_____12. Given the following frequency distribution, the random number 0.1703 would be interpreted as a demand of: Demand Frequency 0 38 1 22 2 22 3 18 a) 0. b) 1. c) 2. d) 3, e) 1 or 2.

______13. The following are two constraints:

;

If and , what are the values for ?

(a) 12,

(b) 6,

(c) 2,

(d) 0,

(e)

_____14. (Given the following small project) When will the project be completed?

Activity

Immediate Predecessor

Time (days)

A

-

8

B

-

7

C

A, B

4

D

B

3

E

C, D

4

a) 14, b) 11, c) 16, d) 20, e) none of the above.

15. The Investment Club at Bell Labs has solicited and obtained $50,000 from its members. Collectively, the members have selected the three stocks, two bond funds, and a tax-deferred annuity shown in the following table as possible investments (let Xi=$ invested in option i, i=1, 2, 3, 4, 5, and 6). Formulate and solve a linear program that will maximize the total projected annual return subject to the conditions set forth by the Investment Club members.

Decision Variable

Investment Option

Risk

Projected Annual Return

X1

Stock – EAL

High

15%

X2

Stock – BRU

Moderate

12%

X3

Stock – TAT

Low

9%

X4

Bonds – long term

11%

X5

Bonds – short term

8%

X6

Tax-deferred annuity

6%

The club members have decided on the following strategies for investment:

· All $50,000 is to be invested.

· At least $10,000 is to be invested in the tax-deferred annuity.

· At least 25% of the funds invested in stocks are to be in the low-risk stock (i.e. TAT).

· No more than $12,500 of the total investment is to be placed in investments with projected annual returns of less than 10% (i.e. TAT, Short term Bonds, and Tax-deferred annuity)

· At least as much is to be invested in bonds as stocks.

_____15. One typo can be found in (a) cell B7, (b) cell B9, (c) cell B18, (d) cell B21, (e) cell D10, (f) I7, (g) none of the above.

_____16. The _____ value for each less-than-or-equal-to constraint indicates the difference between the left-hand and right-hand values for a constraint.

a. objective function coefficient

b. slack

c. unbounded

d. surplus

*** (After Final) Announcement***

Now that the grades are final I will NOT:

Change your grade once that is determined