What is the constraint associated with job A for the following assignment problem?Machine1A $323otherwise 0.$4 $2Job B $1 $3 $5C $6 $4 $2O 3XA1 + 4XA2 + 2XA3 = -1O XA1 - XA2 - XA3 = -1O -XA1 - XA2 - XA3 = +1O 3XA1 + 4XA2 + 2XA3 = 1= 1 if job i is assigned to machine j,Let Xij =

A constraint is a strict restriction placed on a variable's value that stops us from continuing in a…

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 68P

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The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.
Maximize Profit=123 L + 136 S 17 L+11 S≤ 3000 6 L+9 S≤2500 L20 and S20 (Availability of component A) (Availability of component B) Show Transcribed Text Implement the linear optimization model and find an optimal solution. Interpret the optimal solution. The optimal solution is to produce LaserStop models and SpeedBuster models. This solution gives the possible profit, which is $. (Type integers or decimals rounded to two decimal places as needed.)
4. Optimal Rental Decisions in Cloud Computing Assume that AWS has the following 3 options for renting servers. Fraction of Job in one Server Description Rental Low Power Medium Power High Power $2/hr. $4/hr. $9/hr. Hour 1/8 1/6 1/3 L M Note that if you rent a server for less than one hour, you still must pay the rent for the entire hour. You have a job that must finısh in at most 5 hours. The low-power server can finish 1/8th of the job in 1 hour, the medium-power server can finish 1/6 of the job in one hour, and the high- power server can finish 1/3rd of the job in one hour. (a) The typical practice used by most firms is to find a single server that can do the work at the least cost and within the available time. Find the best sıngle server solution-that is, which single server should you use and for how many hours will you rent this server?
variables $E$11 47000 0 35 7.0000001 8.0000001 BO Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $B$16 LHS 55000 41 55000 10500 47000 $B$17 LHS 72000 35 72000 10500 47000 $B$18 LHS 80000 -8 80000 47000 10500 10500 $B$19 LHS 47000 0 57500 1E+30 The answers to the questions are found in this sensitivity report. Questions: Write your responses in the space provided 1. What is the range of optimality for the BN and BO variables? write your answers in this format: Lower limit <= Coefficient of BN <= Upper limit. Example 22 <= C of BN <= 40 2. What is the range of feasibility for the constraints located on B17 and B18? 3. If the right-hand side of the constraint located on B17 is decreased by 200, what is the effect on the value of the objective function?
Calculating outcomes as equally likely would BEST describe: O a. Maximax criterion O b. Laplace criterion O c. Regret criterion Od. Maximin criterion Determining the average payoff for each alternative and choosing the one with the BEST payoff is the approach called: ea, maximax O b. minimax regret O c. laplace Od maximin 2
Suppose my utility function for asset position x is givenby u(x) ln x.a Am I risk-averse, risk-neutral, or risk-seeking? b I now have $20,000 and am considering the follow-ing two lotteries: L1: With probability 1, I lose $1,000.L2: With probability .9, I gain $0.L2: With probability .1, I lose $10,000.Determine which lottery I prefer and the risk premium of L2.
PROBLEM-2 XYZ Company manufactures a number of products. One important product is Q. which consists of two internally manufactured items Rand S as in the figure below: R (1 Piece) ITEM Q R S Item Q is assembled in an assembly station, A 10; Item R is in work center WC 30, and item S is manufactured in work center WC 70. Operation data for product Q and items R and S are shown in the table: ITEM Q Week Gross Requirements Lot size Lot for lot 50 150 1 40 Q Work Center 2 80 A 10 WC 30 WC 70 3 40 S (3 Pieces) 4 30 Setup time (Hrs) 0 3.0 2.0 5 40 6 30 Runtime per piece Lead Time (weeks) (Hrs) 1.7 1.0 1.0 1 1 1 1 Determine "capacity requirements planning" stated for product Q in the work centers A 10, WC 30, and W 70 for the next weeks on the basis of material requirements planning carried out.
Briefly explain these terms:a. Basic variableb. Shadow pricec. Range of feasibilityd. Range of optimality
Maximize p = 7x + 6y + 3z subject to x + y + z ≤ 150 x + y + z ≥ 100 x ≥ 0, y ≥ 0, z ≥ 0. p= (x, y, z)=
Please show how to solve b
Formulate an LP model for the following problems.1. Bernadette intends to invest up to ₱50,000 in either Best Fund, or a time deposit orboth. The Best Fund pays 8% per year and the time deposit pays 9%. Because theBest Fund is riskier than the time deposit, so she intends to put at most ₱30,000 intothe time deposit and at least ₱10,000 into the Best Fund. How much should she allotto each investment in order to maximize her returns?
SIMPLEX METHOD A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftsman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftsman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. If the profit on a racket and on a bat is Php 20.00 and Php 10.00 respectively, find the maximum profit of the factory when it works at full capacity.

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What is the constraint associated with job A for the following assignment problem? Machine 1 2 3 A $3 $4 $2 Job B $1 $3 $5 otherwise 0. C $6 $4 $2 O 3XAI + 4XA2 + 2XA3 = -1 O XA1 -XA2-XA3 = -1 O -XAI - XA2-XA3 = +1 O 3XAI + 4XA2+2XA3 = 1 Let Xij = 1 if job i is assigned to machine j,