Based on Rothstein (1973). The Springfield City Police Department employs 30 police officers. Each officer works five days per week. The crime rate fluctuates with the day of the week, so the number of police officers required each day depends on the day of the week, as follows: Saturday, 28; Sunday, 18; Monday, 18; Tuesday, 24; Wednesday, 25; Thursday, 16; and Friday, 21. The police department wants to schedule police officers to minimize the number whose days off are not consecutive. Determine how to accomplish this goal.

Q: A television station has commercials of the following lengths (in seconds): 15, 20, 25, 30, 40, 45,…

A: For the assignment of known time in a given maximum time, we use the line balancing technique. It is…

Q: 24. Powerco has three electric power plants that supply the needs of four cities. Each power plant…

A:

Q: According to the specifications in the problem, what is the maximum number of shirts that can be…

A: Solution 1: Requirement in Month 1 = 2000 pants So, total cloth requirement in Month 1 = 2000*3 =…

Q: A company produces pants and shirts. Each pants requires three square yards of cloth, and each…

A: Statement Showing the Total and Per Unit Cost Of Each Product…

Q: The Clark County Sheriff’s Department schedules police officers for 8-hour shifts. The beginning…

A: CCS wants to minimize the total number of police officers required in each of six shifts. The…

Q: Each hour from 10 a.m. to 7 p.m., Bank One receives checks and must process them. Its goal is to…

A: Linear programming problem talks about the minimization of cost and maximizing the cost. Companies…

Q: 1. The working system in a hospital is divided into 8 time periods, each of which is 3 hours, as in…

A: Formulate a spreadsheet as shown below to compute the minimum number of doctors while satisfying the…

Q: During each 4-hour period, the Smalltown police force requires the following number of on-duty…

A: Given that, During each 4-hour period, the Smalltown police force requires the following number of…

Q: The Pine Valley Board of Education must hire teachers for the coming school year. The types of…

A: Formulate Goal programming (GP) model as under Decision variables: Let x1, x2, x3, x4, x5, x6 be the…

Q: A company produces pants and shirts. Each pants requires three square yards of cloth, and each…

A: Given data:   Shirt Pant Total Cloth requirement (Sq yards) 3 2   Demand to met for 2 months…

Q: Eastinghouse sells air conditioners. The annual demand for air conditioners in each region of the…

A: Let the following be the representation   Newyork = 1 Atlanta = 2 Chicago = 3 Los Angeles…

Q: 1. Muscat Inc. is working on its cash budget for December. The budgeted beginning cash balance is…

A: [Comment:] Thank you for your questions. Please note per the guidelines, only one multiple-choice…

Q: A large department store operates 7 days a week. The manager estimates that the minimum number of…

A: Given data,  The store operates = 7 days a week  Services prompt  Monday = 12  Tuesday = 18…

Q: City 1 produces 500 tons of waste per day, city 2 produces 400 tons of waste per day, and city 3…

A: Let considered be the tons of city  waste that is sent to incinerator, for. Let…

Q: During each four-hour period, the Smalltown police force requires the following number of on-duty…

A: Given data is Time slot Police officers needed Midnight to 4 a.m. 4 4 a.m. to 8 a.m. 4 8…

Q: Rachel can invest up to$10,000 (USD) in the American stock market. She can invest in stocks and…

A: Let, S is the number of Dollars invested in Stock and  L is the number of Dollars invested in Loan…

Q: Each day, workers at an emergency department work two 6-hour shifts chosen from 12 A.M. to 6 A.M., 6…

A: Given data,  The different shift 1) 12 A.M to 6 A.M 2) 6 A.M to 12 P.M 3) 12 P.M to 6 P.M 4) 6 P.M…

Q: A bank operates from 10 a.m. to 8 p.m. and employs both full-time and part-time workers. Full-time…

A: note: zoom in for clear image     10-11 AM 11A-N N-1P 1P-2P 2P-3P 3P-4P 4P-5P 5P-6P 6P-7P 7P-8P…

Q: steel company has two mills. Mill 1 costs $70,000 per day to operate, and it can produce 400 tons of…

A: Cost refers to an expenditure or expenses incurred by an organization in order to produce and sell…

Q: A manufacturing company makes two products (denoted as X and Y) through two ma- chines (denoted as A…

A: (1) maximize X + Y   subject to   50 X + 24 Y <= 40 hours x 60 minutes per hour   30X +…

Q: A company produces six products in the followingfashion. Each unit of raw material purchased yields…

A: Let P1 and P2 be the number of units of product 1 and 2 respectively to be processed further, S1,…

Q: Niki holds two part-time jobs, Job I and Job II. She never wants to work more than a total of 12…

A: GIVEN THAT: TOTAL HOURS AVAILABLE TO WORK = 12 HRS PER WEEK PREPARATION TIME NEEDED FOR JOB 1= 2 HRS…

Q: Consider Miller Chemicals that produces water purification crystals labor costs are $200,000; raw…

A: The question is related to Productivity. Productivity is the measure of efficicency of production…

Q: An Electrical Utility Startup Problem A problem faced by an electrical utility company each day is…

A: Let us consider the variables A, B, C,D & E represent the Generators A,B,C,D & E. Now, let…

Q: A large department store operates 7 days a week. The manager estimates that the minimum number of…

A: Decision variables: The seven shifts will be required to schedule employees for 5 consecutive days…

Q: A plumbing repair company has 3 employees and must choose which of 3 jobs to assign each to (each…

A: Formula:

Q: A power plant has three boilers. If a given boiler is operated, it can be used to produce a quantity…

A: Given information  Cost of producing = 8000 Kwh  No Minimum Steam   Maximum Steam   Cost /Tons…

Q: During each 4-hour period, the Smalltown police forcerequires the following number of on-duty police…

A: Step-1: Define, decision variables as show below: x1 = number of employees who start working at the…

Q: A manufacturer produces bicycles and motorcycles, each of which must be processed through two…

A:

Q: These constraints translate mathematically to X, 2 .2(x, + x2 + x3 + x4) x2 2 .1(x, + x2 + x3 + x4)…

A:

Q: A company has nine jobs that must be assigned to three ordered workstations. The file P08_39.xlsx…

A: Given data- Now, from cell H4 to H12 take as decision variables to decide that which job will…

Q: A production department requires different numbers of full-time employees on different days of the…

A: Please note we are integrating all the part in to a and B.] a) Min C1X1 + C2X2 + C3X3 + C4X4 + C5X5…

Q: A large department store operates seven days a week. The manager estimates that the minimum number…

A: Decision variable:   Suppose-X1 be the no. of salespersons having off-days on Monday & TuesdayX2…

Q: Formulate an LP

A: For the above question, we can assume the variables as follows: Let X1 be the number of workers who…

Q: Each day, workers at the Gotham City Police Department work two 6-hour shifts chosen from 12 A.M to…

A: Constraint 1                                     x1 + x2 + x3  ≥ 15 Constraint 2…

Q: A bank operates from 10 a.m. to 8 p.m. and employs both full-time and part-time workers. Full-time…

A: 10-11 AM 11A-N N-1P 1P-2P 2P-3P 3P-4P 4P-5P 5P-6P 6P-7P 7P-8P   1 1 1 1 1 1 1 1 1 1…

Q: A farmer in the Midwest has 1,000 acres of land on which she intends to plant corn, wheat, and…

A: Given information,  Cost of Corn = $100  Profit = $30  Cost of Soyabean = $70 Profit = $20  Cost of…

Q: A large department store operates 7 days a week. The manager estimates that the   minimum number of…

A: A Small Introduction about Sales Management   Deals the board is the method involved with getting…

Q: Monroe County is trying to determine where to place the county fire station. The locations of the…

A: This is what is known from the problem: The locations of the county’s four major town are: (10, 20),…

Q: A manufacturing firm produces two products. Each product must undergo an assembly process and a…

A: let the products be A, B suppose the number of units A produced = x the number of units B produced =…

Q: 60. Ford has four automobile plants. Each is capable of producing the Focus, Mustang, or Taurus, but…

A: Given:  The details of plants, fixed cost, cars to be made, the demand of the cars and variable cost…

Q: Bark's Pet Food Company produces canned cat food called Meow Chow and canned dog food called Bow…

A: Linear programming problem is formulated to calculate the quantity required for each category and…

Q: An Automobile company uses three types of steel S1, S2 and S3 for producing three types of cars C1,…

A: Cars/Steel C1 C2 C3 S1 2 3 4 S2 1 1 2 S3 3 2 1 Tons of Steel available S1 = 29 Tons S2 = 13…

Q: A manufacturer produces bicycles and motorcycles, each of which must be processed through two…

A:

Q: 60. Ford has four automobile plants. Each is capable of producing the Focus, Mustang, or Taurus, but…

A: Given data,

Q: A production department requires different numbers of full-time employees on different days of the…

A: a) Min C1X1 + C2X2 + C3X3 + C4X4 + C5X5 + C6X6 + C7X7 Subject to 1X1 + 0X2 + 0X3 + 1X4 + 1X5 + 1X6 +…

Optimization Models

Optimization models are mathematical models that help organizations determine the best way to allocate scarce resources to achieve specific objectives. These models can be used to solve a wide variety of problems, from finding the most efficient route for a delivery truck to determining the optimal mix of products to stock in a store.