MidTerm and HW 4

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OPR xxxx - Fall 2018 Midterm – due dates to be determined page 6 of 6

OPR xxxx - MIDTERM - Takehome

Ideally you should begin working on the exam immediately. It should be completed independently (in an ideal world) by each student. (Since no monitoring process can exist it will be OK for you to discuss the problems with other students in general terms. But you should really do the analysis by yourself. But you must do your own computer work and written submissions) If something is unclear to you about the exam, ask me. Write your name on all pages you submit. Answers without written backup do not have any value; i.e. show your work . Either submit each problem on a separate page or make a summary sheet with your answers. INCLUDE this statement

I, __________________, have not, and will not violate the rules of academic integrity (↑↑↑) on this exam.

(fill in name) Sign here if this statement is true. ________________________________

Question 7 and Question 8 are Extra Credit Questions

1. TAY 226/54

2. (WA 459.7) Gotham City must determine how to allocate ambulances during the next year. It costs $5,000 per year to run an ambulance. Each ambulance must be assigned to one of two districts. Let

x = number of ambulances in district 1

y = number of ambulances in district 2

The average time in minutes for an ambulance to respond to a call is

District 1 40 – 3x

District 2 50 – 4y

Gotham City has three goals (listed in order of priority)

1. At most $100,000 per year should be spent on ambulance service

2. Average response time in district 1 should be at most 5 minutes

3. Average response time in district 2 should be at most 5 minutes

Remember that the number of ambulances must be integer.

a. Use preemptive goal programming to determine how many ambulances to assign to each district.

b. If each minute in extra average response time is worth $4,000 in district 1 and $2,000 in district 2, determine how many ambulances to assign to each district (assuming there are no other priorities among the goals).

3. Hint - This problem is best solved using binary integer variables .

OPR xxxx - Fall 2018 Midterm – 11/5/2018 page 1 of 6

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4. (WA 283.114) Ann and Ben are getting divorced, and they want to determine how to divide up their joint property: retirement account, home, summer cottage, investments, and miscellaneous assets. Ann and Ben are asked to allocate 100 total points to the assets. Their allocation is:

Assuming that all assets are divisible (i.e. a fraction of each asset can be given to each person), how should the assets be allocated? Two criterion appear reasonable:

· Each person should end up with the same number of points. This prevents Ann from envying Ben and vice versa.

· The total number of points received by Ann and Ben should be maximized.

If one or more of the assets could not be split between the two people, how would you modify your solution?

5. TAY 212/23 - NO ALGEBRAIC FORMULATION NEEDED (IGNORE “a” below)

(IGNORE “a” above)

c. Suppose that Ampco were to relax its restrictions that it rent exactly the space it needs every month such that it would rent excess space if it were cheaper. How would this affect the optimal solution?

d. MANAGERIAL REPORT

Prepare a managerial report with the following items:

a. The optimal rental plans and associated costs

b. The cost savings (if any) of changing the policy in “c”

c. A statement of any relevant assumptions that you made.

d. Your relevant Excel output.

6. P&B 312/7&8 Do problems 7 AND 8 below

7. This is a problem that Professor Kannan Mohan and I (Bob Blau) were working on. There is a Conversation Partners Program at Baruch to assist non-native (NN) students in practicing English, improving fluency, building vocabulary, and learning about local culture. Each NN student is paired with a native (or near native) volunteer (V) student as a conversation partner. All students fill out a form (on-line) with the following information:

· Name, address, phone number, …

· Age, class level, …

· Gender (Male or Female)

· NN or V (n students are NN and m students are V)

· Time Slots available (there are 28 half-hour slots for each of the 7 days of the week - 196 in total)

(e.g. Time Slot 7 is 11:00-11:30AM on Monday; 1 means available)

The objective is to match as many NN students with V students as possible with the following restrictions:

· It is only possible to pair students of the same gender

· It is only possible to pair students if they have a common available time slot

Develop a mathematical model (i.e. a formulation; an algebraic representation of the problem) including:

· Define the variables

· Write the constraints

· Write the objective function

You need to (think, and then) describe how you can use the data to determine if two students can be matched.

8. H&H Do Cases 6-4 AND 7-3 below

$C:\Users\BobBl_000\Desktop\Fall 2018 Midterm\Scans\H&H Case 6-4a.jpeg$

$C:\Users\BobBl_000\Desktop\Fall 2018 Midterm\Scans\H&H Case 6-4b.jpeg$

$C:\Users\BobBl_000\Desktop\Fall 2018 Midterm\Scans\H&H Case 7-3.jpeg$

Retirement AccountHomeSummer CottageInvestmentsMiscellaneousTotal

Ann's Points502015105100

Ben's Points4030101010100

Case 3-7

	Kvaal	Zuner	Tsai	Mickey	Rollins
Up	100	0	100	267	100
Stable	400	200	100	153	33
Choice	200	800	100	99	33
Hope	200	0	100	451	34
Release	100	0	600	30	800
	Kvaal	Zuner	Tsai	Mickey	Rollins
Up
Stable
Choice
Hope
Release

Case 7-1

Piece #	Artist	Male/Female	Piece	Include	Collage	Sculpture	Sculpture	Drawing	Drawing	Painting	Painting	Painting	Painting	Painting	Price
				(Yes/No)			Wire	Computer	Pen&Ink	Photo	Cubist	Expressionist	Watercolor	Oil
							Mesh			Realistic
1	Colin Zweibell	Male	Perfection				1								$300,000
2	Colin Zweibell	Male	Burden				1								$250,000
3	Colin Zweibell	Male	The Great Equalizer				1								$125,000
4	Rita Loskey	Female	Chaos Reigns					1							$400,000
5	Rita Loskey	Female	Who Has Control					1							$500,000
6	Rita Loskey	Female	Domestication						1						$400,000
7	Rita Loskey	Female	Innocence						1						$550,000
8	Norm Marson	Male	Aging Earth			1									$700,000
9	Norm Marson	Male	Wasted Resources		1										$575,000
10	CandyTate	Female	Serenity										1		$200,000
11	CandyTate	Female	Calm before the Storm										1		$225,000
12	Robert Bayer	Male	Void											1	$150,000
13	Robert Bayer	Male	Sun											1	$150,000
14	David Lyman	Male	Storefront Window							1					$850,000
15	David Lyman	Male	Harley							1					$750,000
16	Angie Oldman	Female	Consumerism		1										$400,000
17	Angie Oldman	Female	Reflection			1									$175,000
18	Angie Oldman	Female	Trojan Victory			1									$450,000
19	Rick Rawls	Male	Rick							1					$500,000
20	Rick Rawls	Male	Rick II								1				$500,000
21	Rick Rawls	Male	Rick III									1			$500,000
22	Bill Reynolds	Male	Beyond											1	$650,000
23	Bill Reynolds	Male	Pioneers											1	$650,000
24	Bear Canton	Male	Wisdom						1						$250,000
25	Bear Canton	Male	Superior Powers						1						$350,000
26	Bear Canton	Male	Living Land											1	$450,000
27	Helen Row	Female	Study of a Violin								1				$400,000
28	Helen Row	Female	Study of a Fruit Bowl								1				$400,000
29	Ziggy Lite	Male	My Namesake		1										$300,000
30	Ziggy Lite	Male	Narcissism		1										$300,000
31	Ash Briggs	Male	All That Glitters										1		$50,000
32	Ash Briggs	Male	The Rock										1		$50,000
33	Ash Briggs	Male	Winding Road										1		$50,000
34	Ash Briggs	Male	Dreams Come True										1		$50,000

Ann and Ben

	Retirement Account	Home	Summer Cottage	Investments	Miscellaneous	Total
Ann's Points	50	20	15	10	5	100
Ben's Points	40	30	10	10	10	100

StudentName…MaleFemaleTime Slot 1TS-2TS-3…TS-196

NN -1Al1111

NN - 2Betty111

…………………………

NN - nSam1111

V - 1Alice11

V - 2Ben1111

…………………………

V - mSally111