A retail store in Des Moines, Iowa, receives shipments of a particular product from Kansas City and Minneapolis. Let x 5 number of units of the product received from Kansas City y 5 number of units of the product received from Minneapolis a. Write an expression for the total number of units of the product received by the retail store in Des Moines. b. Shipments from Kansas City cost $0.20 per unit, and shipments from Minneapolis cost $0.25 per unit. Develop an objective function representing the total cost of shipments to Des Moines. c. Assuming the monthly demand at the retail store is 5000 units, develop a constraint that requires 5000 units to be shipped to Des Moines. d. No more than 4000 units can be shipped from Kansas City, and no more than 3000 units can be shipped from Minneapolis in a month. Develop constraints to model this situation. e. Of course, negative amounts cannot be shipped. Combine the objective function and constraints developed to state a mathematical model for satisfying the demand at the Des Moines retail store at minimum cost.

A retail store in Des Moines, Iowa, receives shipments of a particular product from Kansas City and Minneapolis. Let x 5 number of units of the product received from Kansas City y 5 number of units of the product received from Minneapolis a. Write an expression for the total number of units of the product received by the retail store in Des Moines. b. Shipments from Kansas City cost $0.20 per unit, and shipments from Minneapolis cost $0.25 per unit. Develop an objective function representing the total cost of shipments to Des Moines. c. Assuming the monthly demand at the retail store is 5000 units, develop a constraint that requires 5000 units to be shipped to Des Moines. d. No more than 4000 units can be shipped from Kansas City, and no more than 3000 units can be shipped from Minneapolis in a month. Develop constraints to model this situation. e. Of course, negative amounts cannot be shipped. Combine the objective function and constraints developed to state a mathematical model for satisfying the demand at the Des Moines retail store at minimum cost.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section: Chapter Questions

Problem 46P

See similar textbooks

Similar questions

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.
Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
Long-Life Insurance has developed a linear model that it uses to determine the amount of term life insurance a family of four should have, based on the current age of the head of the household. The equation is:y = 850 − .1xwherey = Insurance needed ($000)x = Current age of head of household a. Plot the relationship on a graph. b. Use the equation to determine the amount of term life insurance to recommend for a family of four if the head of the household is 30 years old.
Maximize 8x + 9y Subject to -- x + 2 y 0 a) Solve using simplex method
Please show solution and formula used. Assuming the total number of students studying in the top four universities in the Philippines is approximately 158,000. And the distribution is as follows: University of the Philippines (UP) - 40% of the total number Ateneo de Manila University (ADMU) - 23,700 De La Salle University (DLSU) - 25% of the total number University of Santo Tomas - 20% of the total number And only the following number of students owns a tablet computer: 20% of UP students 85% of ADMU students 90% of DLSU students 85% of UST students What is the total market penetration of tablet computers among the students of the top four universities? What is the total market size of tablet computers in the top four universities?
(Use output ranges of 2000, 4000, 6000, 8000 etc. and intervals of $50,000 on the Y axis. Output X Location A Location B Location B Location D 2 000 120 000 120 000 130 000 150 000 4 000 180 000 160 000 160 000 170 000 6 000 240 000 200 000 190 000 190 000 8 000 300 000 240 000 220 000 210 000 10 000 360,000 280 000 250 000 230 000 12 000 420 000 320 000 280 000 250 000 14 000 480,000 360 000 310,000 270 000 16 000 540 000 400 000 340 000 290 000 18 000 600 000 440 000 370 000 310 000 20 000 660 000 480 000 400 000 330 000 Over what range of output is location A the most preferred location? 2. Over what range of output is location B the most preferred location? 3.Over what range of output is location C the most preferred location?
I want answers to points e and f
HMO has 40 doctors to be apportioned among four clinics. The HMO decides to apportion the doctors based on the average weekly patient load for each clinic, given in the following table. Clinic A B C D Average Weekly 275 392 611 724 Patient Load Find the apportion of A and C using using Adam's Method. Use modified divisor 52. Doctors for clinic A Doctors for clinic B = %3D Doctors for clinic C= Doctors for clinic D =
Using the grid technique to determine the least-cost location (warehouse) for this problem: Tons Rate X - Coordinates Y – Coordinates S1 200 0.5 2 14 S2 300 0.6 6 10 M1 100 1 2 2 M2 100 2 10 14 M3 100 1 14 18 M4 100 2 14 6 The Grid center coordination is ____ and _____ (round the results to 1 decimal place) Group of answer choices (9.9; 7.8) (5.5; 6.9) (8.7; 10.5) (10.5; 6.4) (9.9; 8.9)
solve for y in part b
J 2 An electronics store wants to identify a location for a warehouse that will ship to five retail stores. The coordinates and annual number of truckloads are given in the accompanying table. Develop a model to find the best location, assuming that straight-line distances can be used between the locations. Experiment with the model by testing each of the possible best solutions, included, to find the best location. Click here to view the data for the store locations and annual numbers of truckloads. Click here to view some possible best solutions. The best location is at____. (Type an ordered pair. Round each coordinate to the nearest integer as needed.)
In the past, Peter Kelle's tire dealership in Baton Rouge sold an average of 1,000 radials each year. In the past 2 years, 220 and 250, respectively were sold in fall, 360 and 320 in winter, 145 and 175 in spring, and 300 and 230 in summer. With a major expansion planned, Kelle projects sales next year to increase to 1,200 radials. Based on next year's projected sales, the demand for each season is going to be (enter your responses as whole numbers): Season Demand Fall nothing