A company makes 2 different types of gloves; a regular type and a professional type. The company has 900 hours of production time available in its cutting and sewing department; 300 hours available in its finishing department; and 100 hours available in its packaging and shipping department. To make each regular type glove requires 1 hour in the cutting and sewing department; 0.5 hours in the finishing department; and 0.143 hours in the packaging and shipping department. To make each professional type glove requires 1.5 hours in the cutting and sewing department; 0.33 hours in the finishing department; and 0.143 hours in the packaging and shipping department. if the company makes a profit of $5 on each regular type glove, and $8 on each professional type glove, how many of each glove should the company manufacture in order to maximize its profit?

A company makes 2 different types of gloves; a regular type and a professional type. The company has 900 hours of production time available in its cutting and sewing department; 300 hours available in its finishing department; and 100 hours available in its packaging and shipping department. To make each regular type glove requires 1 hour in the cutting and sewing department; 0.5 hours in the finishing department; and 0.143 hours in the packaging and shipping department. To make each professional type glove requires 1.5 hours in the cutting and sewing department; 0.33 hours in the finishing department; and 0.143 hours in the packaging and shipping department. if the company makes a profit of $5 on each regular type glove, and $8 on each professional type glove, how many of each glove should the company manufacture in order to maximize its profit?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 79P

See similar textbooks

Similar questions

Southern Sporting Goods Company makes basketballs and footballs. Each product is produced from two resources—rubber and leather. The resource requirements for each product and the total resources available are as follows: Product Rubber (lb.) Leather (ft.2) Basketball 3 4 Football 2 5 Total resource available 500 lb. 800 ft.2 Each basketball produced results in a profit of $12, and each football earns $16 in profit. 1) Formulate a linear programming model to determine the number of basketballs and footballs to produce in order to maximize profit. Transform this model into standard form.
For this linear programming problem, formulate the linear programming model. Then, find the optimal solution graphically for the LP with only 2 variables. i.e: Max Z = 500x + 300y Subject to: 4x + 2y <= 60 (1st constraint) 2x + 4y <= 48 (2nd constraint) x, y >= 0 (non-negativity) A construction company manufactures bags of concrete mix from beach sand and river sand. Each cubic meter of beach sand costs ₽60 and contains 4 units of fine sand, 3 units of coarse sand, and 5 units of gravel. Each cubic meter of river sand costs ₽100 and contains 3 units of fine sand, 6 units of coarse sand, and 2 units of gravel. Each bag of concrete must contain at least 12 units of fine sand, 12 units of coarse sand, and 10 units of gravel. Find the best combination of beach sand and river sand which will meet the minimum requirements of fine sand, coarse sand, and gravel at the least cost.
For this linear programming problem, formulate the linear programming model. Then, find the optimal solution graphically for the LP with only 2 variables. Max Z = 500x + 300y Subject to: 4x + 2y <= 60 (1st constraint) 2x + 4y <= 48 (2nd constraint) x, y >= 0 (non-negativity) A farmer has 5 hectares of land to plant with rice and corn. He needs to decide how many hectares of rice and corn to plant. He can make ₽200,000 profit per hectare planted to rice and ₽250,000 profit per hectare planted with corn. However, the corn takes 2 hours of labor per hectare to harvest and the rice takes 1 hour per hectare. The farmer has 8 hours of labor to harvest. To maximize his profit, how many hectares of each should he plant? *additional note: philippine peso is used as currency :)*
The problem below involves three variables. Solve it with the simplex method, Excel, or some other technology.A contractor builds three types of houses: the Aries, the Belfair, and the Wexford. Each house requires one lot, and the following table gives the number of labor-hours and the amount of capital needed for each type of house, as well as the profit on the sale of each house. There are 13 lots, 52,400 labor-hours, and $3,684,200 available for the contractor's use. Aries Belfair Wexford Labor-hours 3,000 3,700 5,000 Capital $205,000 $279,600 $350,000 Profit $20,000 $25,000 $30,000 (a) Building how many of each type of house will maximize his profit? Aries houses Belfair houses Wexford houses (b) What is the maximum possible profit?$
Solve the following linear programming problem using simplex method. A diet for a sick person must contain at least 4000 units of vitamins, 50 units of minerals and 1400 of calories. Two foods A and B are available at a cost of Rs. 4 and Rs. 3 per unit respectively. If one unit of A contains 200 units of vitamins 1 unit of mineral and 40 calories and one unit of food B contains 100 units of vitamins, 2 units of minerals and 40 calories, find by simplex method what combination of Foods be used to have least cost.
Consider the following all-integer linear program. Max 5x1 + 8x2 s.t. 6x1 + 5x2 ≤ 25 10x1 + 4x2 ≤ 40 1x1 + 2x2 ≤ 8 x1, x2 ≥ 0 and integer (a) Graph the constraints for this problem. Use points to indicate all feasible integer solutions. (b) Find the optimal solution to the LP Relaxation. (Round your answers to three decimal places.) at (x1, x2) = Using this solution, round down to find a feasible integer solution. at (x1, x2) = (c) Find the optimal integer solution. at (x1, x2) = Is it the same as the solution obtained in part (b) by rounding down? YesNo
Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 52 units of synthetic fiber, requires 28 hours of production time, and needs 22 units of foam backing. Each roll of Grade Y carpet uses 45 units of synthetic fiber, requires 30 hours of production time, and needs 16 units of foam backing.The profit per roll of Grade X carpet is $205 and the profit per roll of Grade Y carpet is $155. In the coming production period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility. This means that instead of using the = or ≤ sign in the constraint you should use the ≥ sign.). The company has 1500 units of foam backing available for use.Develop and solve a linear programming model…
Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 52 units of synthetic fiber, requires 28 hours of production time, and needs 22 units of foam backing. Each roll of Grade Y carpet uses 45 units of synthetic fiber, requires 30 hours of production time, and needs 16 units of foam backing.The profit per roll of Grade X carpet is $205 and the profit per roll of Grade Y carpet is $155. In the coming production period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility. This means that instead of using the = or ≤ sign in the constraint you should use the ≥ sign.). The company has 1500 units of foam backing available for use.Develop and solve a linear programming model…
The manager of the Ewing and Barnes Department Store has four employees available to assign to three departments in the storelamps, sporting goods, and linens. The manager wants each of these departments to have at least one employee, but not more than two. Therefore, two departments will be assigned one employee, and one department will be assigned two. Each employee has different areas of expertise, which are reflected in the daily sales each employee is expected to generate in each department, as follows: The manager wishes to know which employee(s) to assign to each department in order to maximize expected sales. a. Formulate a linear programming model for this problem. b. Solve the model by using the computer. c. Suppose that the department manager plans to assign only one employee to each department and to lay off the least productive employee. Formulate a new linear programming model that reflects this new condition and solve by using the computer.
BS Oil manages a refinery in the Gulf of Mexico. The refinery distills crude oil from two sources, Country A and Country B, into three main products: kerosene, asphalt base, and petroleum naphtha. The two Countries' oil differs in composition and therefore contains different chemical mixes. Each barrel of Country A’s crude oil yields 0.3barrel of kerosene, 0.4 barrels of asphalt base, 0.2 barrels of petroleum naphtha, and 0.1 barrels of waste. On the other hand, each barrel of Country B’s crude oil yields 0.4 barrels of kerosene,0.2 barrels of asphalt base, 0.3 barrels of petroleum naphtha, and 0.1 barrels of waste. The crude oils also differ in cost and availability. BS Oil can purchase up to 9000 barrels per day from Country A at$20 per barrel. Up to 6000 barrels per day of Country B are also available at the lower cost of$15 per barrel because of shorter transportation costs. BS Oil contracts with independent distributors require it to produce at least 2000 barrels per day of…
BS Oil manages a refinery in the Gulf of Mexico. The refinery distills crude oil from two sources, Country A and Country B, into three main products: kerosene, asphalt base, and petroleum naphtha. The two Countries' oil differs in composition and therefore contains different chemical mixes. Each barrel of Country A’s crude oil yields 0.3barrel of kerosene, 0.4 barrels of asphalt base, 0.2 barrels of petroleum naphtha, and 0.1 barrels of waste. On the other hand, each barrel of Country B’s crude oil yields 0.4 barrels of kerosene,0.2 barrels of asphalt base, 0.3 barrels of petroleum naphtha, and 0.1 barrels of waste. The crude oils also differ in cost and availability. BS Oil can purchase up to 9000 barrels per day from Country A at$20 per barrel. Up to 6000 barrels per day of Country B are also available at the lower cost of$15 per barrel because of shorter transportation costs. BS Oil contracts with independent distributors require it to produce at least 2000 barrels per day of…
Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 50 units of synthetic fiber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade Y carpet uses 40 units of synthetic fiber, requires 28 hours of production time, and needs 15 units of foam backing.The profit per roll of Grade X carpet is $200 and the profit per roll of Grade Y carpet is $160. In the coming production period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility). The company has 1500 units of foam backing available for use.Develop a linear programming model for this problem.1. Define the Decision Variables2. Write the Objective3. Write the Constraints