A firm is attempting to minimize its shipping costs. The firm has 3 factories and must supply the needs of its 3 customers without shortages. Since the firm has no storage facilities, each factory must make daily shipments to its customers. The table below shows the capacity of each factory, the amount required by each customer, and the cost of shipping from each factory to each customer. Shipping Costs ($/unit) Factory/Capacity A/150 units B/150 units C/180 units Customer 1 Customer 2 Customer 3 8 7 15 11 10 15 10 Requirement-240 units Requirement-80 units Requirement-160 units Complete the table below to show the quantity shipped from each factory to each customer. (Leave no cells blank - be certain to enter "O" wherever required.) Shipping Costs ($/unit) Factory Customer 1 Customer 2 Customer 3 A C What is the total cost of meeting customer requirements each day? Total cost

A firm is attempting to minimize its shipping costs. The firm has 3 factories and must supply the needs of its 3 customers without shortages. Since the firm has no storage facilities, each factory must make daily shipments to its customers. The table below shows the capacity of each factory, the amount required by each customer, and the cost of shipping from each factory to each customer. Shipping Costs ($/unit) Factory/Capacity A/150 units B/150 units C/180 units Customer 1 Customer 2 Customer 3 8 7 15 11 10 15 10 Requirement-240 units Requirement-80 units Requirement-160 units Complete the table below to show the quantity shipped from each factory to each customer. (Leave no cells blank - be certain to enter "O" wherever required.) Shipping Costs ($/unit) Factory Customer 1 Customer 2 Customer 3 A C What is the total cost of meeting customer requirements each day? Total cost

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 80P

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Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)
A plant has sufficient capacity to manufacture any combination of four different products (A, B, C, D).For each product, time is required to be invested in four different machines, which is expressed in hours per kilogram of product, as shown in the following table as shown in the following table: (image) Each machine has an availability of 60 hours per week. Products A, B, C and D can be sold at $9, $7, $6 and $5per kilo, respectively. Variable labor costs are $2 per hour for machines 1 and 2, and $3 per hour for machines 3 and 4. The material costs for each kilogram of product A are $4. The material costs for each kilogram of products B, C, D and D are $4 each kilogram of products B, C and D are $1. What needs to be done:Formulate a profit-maximizing PL model given the maximum demand per product shown in the table (there are 16 variables). Note: it is not necessary to solve the exercise, simply state the exercise
Please use excel for this problem A furniture manufacturer produces two types of tables – country and contemporary – using three types of machines. The time required to produce the tables on each machine is given in the following table: Machine Country Contemporary Total Machine Time Available Per Week Router 3.5 4.0 1,000 Sander 4.5 6.5 2,000 Polisher 3.0 2.0 1,500 Country tables sell for $395 and contemporary tables sell for $515. Management has determined that at least 25% of the tables made should be country and at least 38% should be contemporary. How many of each type of table should the company manufacture if it wants to maximize its revenue? Formulate an LP model for this problem Create the spreadsheet model and use Solver to solve the problem.
An enterprise produces P1, P2 and P3 products using H1 and H2 raw materials. Production data are presented in the table below. The labor time per unit of P1 product is twice that of P2 and three times that of P3. The entire workforce of the production facility is enough to produce 1500 units of P1 product. The market requirement for products is in the order of 3: 2: 5. Establish the Linear programming (DP) model that will maximize the profits of the business and determine the best production quantities?
Hoosier Power needs to determine a capacity expansion plan to meet Bloomington’s power needs for the next 20 years. The current capacity is 5000 kwh. The demand for the current year is 4000 kwh, and demand is expected to increase by 1000 kwh in each succeeding year. At the beginning of each year, Hoosier Power must determine the amount of capacity to add, given the following inputs: ■ Any year in which capacity is added, a fixed cost of $120,000 is incurred plus a cost of $120 per kwh of capacity. ■ At most 10,000 kwh of capacity can be added in a single year. ■ It costs $25 per year to maintain a unit of capacity. ■ It costs $12 per year to produce a kwh. ■ If production does not meet demand, a shortage cost of $80 per kwh short is incurred. Develop a linear integer model to help Hoosier Power minimize its costs for the next 20 years.
A plant has sufficient capacity to manufacture any combination of four different products (A, B, C, D). For each product, time is required to be invested in four different machines, which is expressed in hours per kilogram of product, as shown in the following table as shown in the following table: (attached image) Each machine has an availability of 60 hours per week. Products A, B, C and D can be sold at $9, $7, $6 and $5per kilo, respectively. Variable labor costs are $2 per hour for machines 1 and 2, and $3 per hour for machines 3 and 4. The material costs for each kilogram of product A are $4. The material costs for each kilogram of products B, C, D and D are $4 each kilogram of products B, C and D are $1. What needs to be done:Formulate a profit-maximizing PL model given the maximum demand per product shown in the table (there are 16 variables). Note: The picture is in spanish, but I mean... is pretty easy to understand
A plant has sufficient capacity to manufacture any combination of four different products (A, B, C, D). For each product, time is required to be invested in four different machines, which is expressed in hours per kilogram of product, as shown in the following table as shown in the following table: (attached image) Each machine has an availability of 60 hours per week. Products A, B, C and D can be sold at $9, $7, $6 and $5per kilo, respectively. Variable labor costs are $2 per hour for machines 1 and 2, and $3 per hour for machines 3 and 4. The material costs for each kilogram of product A are $4. The material costs for each kilogram of products B, C, D and D are $4 each kilogram of products B, C and D are $1. What needs to be done:Formulate a profit-maximizing PL model given the maximum demand per product shown in the table (there are 16 variables). Note: do the exercise by hand, or do it digitally, but not in excel.
Given this linear programming model, solve the model and then answer the questions that follow. Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc. Subject to Machine: 5x 1 + 4x 2 + 3x 3 ≤ 160 minutes Labor: 4x1 + 10x2 + 4x3 ≤ 288 hours Materials: 2x 1 + 2x2 + 4x3 ≤ 200 pounds Product 2: x2 ≤ 16 units x1, x2, x3 ≥ 0 a) Are any constraints binding? If so, which one(s)? b) If the profit on product 3 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. c) If the profit on product 1 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. d) If 10 hours less of labor time were available, what would the values of the decision variables be? The objective function? Explain. e) If the manager decided that as many as 20 units of product 2 could be produced (instead of 16), how much additional profit would be generated? f) If profit per unit on each…
Par, Inc., produces a standard golf bag and a deluxe golf bag on a weekly basis. Each golf bag requires time for cutting and dyeing and time for sewing and finishing, as shown in the following table: Hours Required per Bag Product Cutting and Dyeing Sewing and Finishing Standard Bag 1/2 1 Deluxe Bag 1 2/3 The profits per bag and weekly hours available for cutting and dyeing and for sewing and finishing are as follows: Product Profit per Unit ($) Standard Bag $15 Deluxe Bag $8 Activity Weekly Hours Available Cutting and Dyeing 300 Sewing and Finishing 360 Par Inc. will sell whatever quantities it produces of these two products. The aim of the objective function for Par Inc., should be to maximize the objective value. The optimum solution is: Number of standard bags produced per week = 360 (enter your response as a whole number). Number of deluxe bags produced per week =____ (enter…
Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows: Supplier Component 1 2 3 1 $12 $12 $15 2 $11 $10 $12 Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows: Supplier 1 2 3 Capacity 575 950 800 If the Edwards production plan for the next period includes 1050 units of component 1 and 775 units of component 2, what purchases do you recommend? That is, how many units of each component should be…