During each 4-hour period, the Smalltown police force requires the following number ofon-duty police officers: 12midnight to 4 A.M.-8; 4 to 8 A.M.–7; 8 A.M. to 12 noon-6;12 noon to 4 P.M.- 6; 4 to 8 P.M.–5; 8 P.M. to 12 mid night 4. Each police officer workstwo consecutive 4-hour shifts. Formulate an LP that can be used to minimize the number ofpolice officers needed to meet Smalltown's daily requirements.

We suppose, x1=number of police officers starting at shift 1x2=number of police officers starting at…

Answered: During each 4-hour period, the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In her last semester at SPC, Polly Hedron needs to take Statistics and Composition 2. Because Polly is registering early, she has 19 choices for her section of Statistics and 15 choices for her section of Composition. From how many possible schedules can Polly choose? (You may presume that none of these sections interfere with each other) Your Answer: Answer
STAR Co. provides paper to smaller companies with volumes that are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established. Min s.t. 12-ft Pattern Number 15-ft 30-ft 1 2 P1, P2, P3 P4 P5 ≥ 0 3 4 5 12-ft 15-ft 30-ft Trim Loss (ft) 0 0 8 3 7 6 0 0 0 1 C 3 0 2 0 10 Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 3(12) + 0(15) + 2(30) = 96 feet used results in 100 - 96 = 4 foot of trim loss). Orders in hand for the coming week are 5,680 12- foot rolls, 1,690 15-foot rolls, and 3,360 30-foot rolls. Any of the three types of rolls produced in excess of the orders in hand will be sold on the open market at the selling price. No inventory is held. 10 Formulate an integer programming model that will determine how many 100-foot rolls to cut…
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A Hippogriff is a magical beast that had the front legs, wings, and head of a giant eagle and the body, hind legs and tail of horse. It is very similar to another magical creature, the Griffin, with the horse rear replacing the lion rear. A slightly different breed of Hippogriffs, living in the Rathlin Island-the northernmost point in Northern Ireland, has an initial population of No. From that initial population count, it grew to 705 individuals after 28 years. After 28 more years, the population of hippogriffs in Rathlin Island rose to 2764 individuals. If the carrying capacity of Rathlin Island for this particular specie is 3000 individuals, and calculate for the initial population and the growth rate constant of the said species.
Mexico City Bank of Commerce and Industry is a busy bank. Due to different customers' needs, it needs to assign a different number of tellers at the counter at different times of each day. The table below indicates the number of bank Employees/tellers needed at different hours of a day (from 9 am. to 5 pm) at one of its branches. The branch will hire two different types of Employees/tellers: Full-time Teller and Part-time Tellers. The following is a summary of the info. в Етployees Full-time Employees: The bank currently has employed 18 Full time tellers/employees. Full-time tellers that work from 9 a.m. to 5 p.m. Each full-timer will be paid $85 per day on average. The 18 employees can't be layoff. However, the manager may use only Part of the 18 Full-Time Employees in this branch and relocate the rest to another branch with a relocation-related cost $10 per-employee per-day. That is, the employees to be relocated to another department will cost this department $10, instead of $85, a…
A company makes three components for sale. The components are processed on two machines: a shaper and a grinder. The time required. (in minutes) on each machine are as follows: Component Shaper Time Grinder Time A 6 4 B 4 5 C 4 2 The shaper is available for 7200 min. and grinder for 6600 min. No more than 200 units of component C can be sold, but up to 1000 units of each of the other components can be sold. In fact the company has orders for 600 units of component A that must be satisfied. The profit contributions for components A, B and C are $8, $6 and $9 respectively. Formulate the problem for deciding the production quantities. Solve the problem using Excel Solver. Run the sensitivity analysis report in Excel Solver. What are the objective coefficient ranges (Range of Optimality) for each coefficient. Interpret these. What are the dual prices for each constraint? Interpret these. What are the right-hand side ranges (Range of Feasibility)? Interpret them. If more time is…
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Turnover is planned at 2.5 for the six-month peris starting February 1 through July 31. Average weekly sales for that period are $75,000. What average stock should be carried in this situation? $800,000 $900,000 O $720,000 $780,000
In her last semester at SPC, Polly Hedron needs to take Statistics, Composition 2, and Ethics. Because Polly is registering early, she has 14 choices for her section of Statistics, 14 choices for her section of Composition, and 13 choices for her section of Ethics. From how many possible schedules can Polly choose? (You may presume that none of these sections interfere with each other)
Every day, secret, over-worked employees at Wayne Enterprises work two 6-hour shifts producing Batmobiles. These shifts are selected from 12 am - 6 am, 6 am - 12 pm, 12 pm - 6 pm, and 6 pm - 12 am. The following table depicts the number of employees needed during each shift: Shift Time Period 1 2 3 4 12 am - 6 am 6 am - 12 pm 12 pm - 6 pm 6 pm - 12 am Number of Employees Required 13 21 17 11 Bruce Wayne pays all employees working two consecutive shifts, $12 per hour (Note: employees scheduled to work 12 am - 6 am and 6 pm - 12 am would be considered consecutive). Employees whose shifts are not consecutive are paid $18 per hour for the inconvenience. Formulate an LP that can be used to minimize the cost of meeting the daily workforce demands for Batmobile production. To formulate the model, use the following decision variables: Xij = workers working shifts i and j where i, j = {1, 2, 3, 4}
The Cheery Cherry Chair Company makes three types of chairs, the Montegue, the Capulet, and the Verona. Each chair requires assembly, finishing, and a certain amount of wood to make. The assembly area can be used for at most 10 hours per day. To keep him busy, the finishing person needs to work at least 6 hours per day. Producing a Montegue requires 1 hour of assembly, 2 hour of finishing, and 9 board feet of wood. Producing a Capulet requires 1 hour of assembly, 1 hour of finishing, and 9 board feet of wood. Finally, producing a Verona requires 2 hour of assembly, 1 hour of finishing, and 3 board feet of wood. If the company wants to minimize the amount of cherry wood used, how many should they make of each model? (It is possible to complete a fractional part a chair in a given day; in the long run you end up with completed chairs.) Number of Montegues = Number of Capulets = Number of Veronas = How many board feet of cherry wood would be used each day?

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