Kimo's Material Company hauls gravel to a construction site, using a small truck and a large truck. The carryingcapacity and operating cost per load are given in the accompanying table. Kimo must deliver a minimum of 720 cubicyards per day to satisfy her contract with the builder. The union contract with her drivers requires that the totalnumber of loads per day is a minimum of 10. How many loads should be made in each truck per day to minimize thetotal cost?Capacity (yd³)Cost per LoadSmall Truck Large Truck8090$69$58In order to minimize the total cost, the number of loads in a small truck that should be made isloads in a large truck that should be made isand the number of

Let's say x is the total number of loads that fit in a small vehicle and y is the total number of…

Answered: Kimo's Material Company hauls gravel to…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter10: Introduction To Simulation Modeling

Section: Chapter Questions

Problem 35P: Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season....

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ProHaul specializes in trans-American shipments for businesses through the delivery of containers. For every container the company loads on its trucks, ProHaul estimates the haul costs $1,000. In addition, containers are weighed and for each pound, there are hauling fees of $0.15. ProHaul plans to charge $0.49 per pound to his customers.How many pounds would a container have to hold in order for the company to Break Even?
A carpenter produces chairs, tables, and windows. The following information is provided: Cost of production per unit of chairs, tables, and windows is 2, 4, and 6 respectively, and can be sold at 7, 10, and 12, respectively. Weekly demand on chairs, tables, and windows is expected to not exceed 400, 200, and 100, respectively. Production of the three products requires wood, metal sheets and paint. The following table shows the unit requirement of each of the three materials needed and the availability of each. Chairs Tables Windows Weekly availability Wood 2 3 7 1000 Metal Sheets 1 - 1 400 Paint 3 5 10 2000 Production of tables may not exceed twice the units produced of chairs. Total production budget is expected to be 10,000 Pounds every week. Formulate the linear programming model to determine the number of units to produce of the three products such that the net profit is maximized.
The Grand Valley Company, run by the J. Motwani family, produces two products: bed mattresses and box springs. A prior contract requires that the firm produce at least 30 mattresses or box springs, in any combination, per week. In addition, union labor agreements demand that stitching machines be kept running at least 40 hours per week, which is one production period. The firm plans to purchase four machines. Each box spring takes 2 hours of stitching time, while each mattress takes 1 hour on the machine. The firm believes that it can sell at least twice as many mattresses as box springs. Each mattress produced cost $20 and each box spring costs $24. Formulate this problem as a linear programming problem. Summarize the information in this problem into a table similar to table 1, page 701. Formulate the problem as a linear programming problem ( i.e., Write the standard mathematical format).
each Distributors packages and distributes industrial supplies. A standard shipment can be packaged in a class A container, a class K container, or a class T container. A single class A container yields a profit of $10; a class K container, a profit of $8; and a class T container, a profit of $12. Each shipment prepared requires a certain amount of packing material and a certain amount of time. Formulate and solve this problem using LP software. Resources Needed per Standard Shipment Class of Container Packing Material (pounds) Packing Time (hours) A 2 2 K 1 6 T 3 4 Total amount of resource available per week 120 pounds 210 hours Hugh Leach, head of the firm, must decide the optimal number of each class of container to pack each week. He is bound by the previously mentioned resource restrictions but also decides that he must keep his 6 full-time packers employed all 210 hours (6 workers × 35 hours)…
Food Goblin Supermarkets use both cashiers and baggers to serve customers at check out. During the first 6 hours of each workday (Monday–Friday), 4 cashiers and 2 baggers serve approximately 20 customers per hour. A cashier and a bagger who require approximately 5 minutes at checkout and 5 minutes at bagging serve each customer. a. Calculate the utilization of both cashiers and baggers. b. Assume that both baggers and cashiers are cross-trained to perform both activities so that they can serve customers independently. Customers are now both checked and their groceries bagged by one individual. Further, assume that it takes 12 minutes for one individual to both cash out and bag each customer’s groceries. Calculate the utilization of this new group of 6 cross-trained employees.
Nature's Garden Inc. produces wood chips, wood pulp, and mulch. These products are produced through harvesting trees and sending the logs through a wood chipper machine. One batch of logs produces 20,304 cubic yards of wood chips, 14,100 cubic yards of mulch, and 9,024 cubic yards of wood pulp. The joint production process costs a total of $32,000 per batch. After the split-off point, wood chips are immediately sold for $25 per cubic yard while wood pulp and mulch are processed further. The market value of the wood pulp and mulch at the split-off point is estimated to be $22 and $24 per cubic yard, respectively. The additional production process of the wood pulp costs $5 per cubic yard, after which it is sold for $30 per cubic yard. The additional production process of the mulch costs $4 per cubic yard, after which it is sold for $32 per cubic yard.
Bag Company produces leather jackets and handbags. A jacket requires of leather and a handbag only . The labor requirements for the two products are 12 and 5 hours respectively. The current weekly supplies of leather and labor are limited to and 1,850 hours. The company sells the jackets for $350 and the handbags for $120. The objective is to determine the production schedule that maximizes the net revenue. In this document, write the mathematical formulation of both the primal and the dual problems. In the Excel file used in problem 1, solve the primal problem and generate a Solver sensitivity report in a new worksheet. In this document, use the Solver sensitivity report to answer the following two questions: What is the maximum purchase price the company should pay for additional leather? What is the maximum amount the company should pay for additional labor?
The Deeper Furniture makes two products: table and chairs, which must be processed through the assembly and finishing departments. Assembly department is available for 60 hours and in every production period, while the finishing department is available for 48 hours of work. Manufacturing one (1) table requires 4 hours in the assembly and 2 hours in the finishing. Each chair requires 2 hours in the assembly and 4 hours in the finishing. One table contributes P180 to profit, while a chair contributes P100. The problem is to determine the number of tables and chairs to make per production period in order to maximize the profit. Determine the following: A. Define the objective function, formulate the constraints, and graph the system.B. Determine and write the feasible comer points and corresponding profit and the optimal solution. OWN SOLUTIONS FOR UPVOTE. DO NOT USE AI OR ELSE DOWNVOTE.
Weenies and Buns is a food processing plant which manufactures hot dogs and hot dog buns. They grind their own flour forthe hot dog buns at a maximum rate of 200 pounds per week. Eachhot dog bun requires 0.1 pound of flour. They currently have a contract with Pigland, Inc., which specifies that a delivery of 800pounds of pork product is delivered every Monday. Each hot dogrequires pound of pork product. All the other ingredients in thehot dogs and hot dog buns are in plentiful supply. Finally, the laborforce at Weenies and Buns consists of 5 employees working fulltime (40 hours per week each). Each hot dog requires 3 minutes oflabor, and each hot dog bun requires 2 minutes of labor. Each hotdog yields a profit of $0.80, and each bun yields a profit of $0.30.Weenies and Buns would like to know how many hot dogsand how many hot dog buns they should produce each week so asto achieve the highest possible profit.(a) Formulate a linear programming model for this problem.D,I (b) Use the…
A brewery produces regular beer and a lower-carbohydrate Tight beer. Steady customers of the brewery buy 12 units of regular beer and 16 units of light beer monthly. While setting up the brewery to produce the beers, the management decides to produce extra beer, beyond that needed to satisfy customers. The cost per unit of regular beer is $32,000 and the cost per unit of light beer is $60,000. Every unit of regular beer brings in $100,000 in revenue, while every unit of light beer brings in $300,000 in revenue. The brewery needs at least $9,000,000 in revenue, and has determined that the total demand will be at least 50 units of beer. Complete parts (a) and (b).
Pullman Tire Company would like to plan production for the next three months.The firm can satisfy demand by using inventory, regular production (at $40 per tire), overtime (at $50 per tire), or subcontracting (at $70 per tire). Any tires held over for one month incur a $2 per tire inventory carrying cost. Pullman Tire has sufficient regular production capacity to produce up to 700 tires each month, and it can produce up to 50 more tires each month using overtime. The subcon- tracting availability from an alternative supplier is 150 in January and February and 130 in March. Customers will demand 650 tires in January, 1,000 in Febru- ary, and 890 in March (all demand must be satisfied on time; i.e., no backorders are allowed). The firm begins with 100 tires and wants to have no tires left in inventory at the end of March. Formulate a linear program for this problem, and determine the cheapest tire production plan after solving the problem in Excel. This is the answer but I am unsure how…
The town of Lexington purchases gasoline from threevendors to fuel its fleet of municipal vehicles. Each vendordelivers gasoline in 6,000 gallon quantities. Since vendorsmust deliver the fuel, a transportation fee (based on thedistance the vendor must travel) is added to each delivery.The number of deliveries required by each location, the costof supplying a truckload of gasoline to each location fromeach vendor, and the number of truckloads each vendor candeliver are provided below:Assuming that the price per gallon of fuel is the same for eachvendor, develop a linear programming model that minimizesthe total transportation fee that Lexington must pay forsupplying all of its facilities’ fuel needs

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