Question

Linear Programming: A craftswoman produces two products: floor lamps and table lamps. Production of one floor lamp requires 75 minutes of her labor and materials that cost P250. Production of one table lamp requires 50 minutes of labor, and the materials cost P200. The craftswoman wishes to work no more than 40 hours each week, and her financial resources allow her to pay no more than P9,000 for materials each week. She can sell as many lamps as she can make and her profit is P390 per floor lamp and P330 per table lamp. 1. Identify the variables. 2. Set up the objective function. 3. Give the constraints in mathematical expression. 4. Graph the constraints and identify the solution. 5. How many floor lamps and how many table lamps should she make each week to maximize her weekly profit? 6. What is that maximum profit per week?

          Linear Programming:

A craftswoman produces two products: floor lamps and table lamps. Production of one floor lamp requires 75 minutes of her labor and materials that cost P250. Production of one table lamp requires 50 minutes of labor, and the materials cost P200. The craftswoman wishes to work no more than 40 hours each week, and her financial resources allow her to pay no more than P9,000 for materials each week. She can sell as many lamps as she can make and her profit is P390 per floor lamp and P330 per table lamp.

1. Identify the variables.
2. Set up the objective function.
3. Give the constraints in mathematical expression.
4. Graph the constraints and identify the solution.
5. How many floor lamps and how many table lamps should she make each week to maximize her weekly profit?
6. What is that maximum profit per week?

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Linear Programming:

A craftswoman produces two products: floor lamps and table lamps. Production of one floor lamp requires 75 minutes of her labor and materials that cost P250. Production of one table lamp requires 50 minutes of labor, and the materials cost P200. The craftswoman wishes to work no more than 40 hours each week, and her financial resources allow her to pay no more than P9,000 for materials each week. She can sell as many lamps as she can make and her profit is P390 per floor lamp and P330 per table lamp.

1. Identify the variables.
2. Set up the objective function.
3. Give the constraints in mathematical expression.
4. Graph the constraints and identify the solution.
5. How many floor lamps and how many table lamps should she make each week to maximize her weekly profit?
6. What is that maximum profit per week?

Added by Ruben P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/30/2022

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Identify the variables: Let's denote the number of floor lamps she makes as x and the number of table lamps as y. Show more…

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Linear Programming: A craftswoman produces two products: floor lamps and table lamps. Production of one floor lamp requires 75 minutes of her labor and materials that cost P250. Production of one table lamp requires 50 minutes of labor and the materials cost P200. The craftswoman wishes to work no more than 40 hours each week, and her financial resources allow her to pay no more than P9,000 for materials each week. She can sell as many lamps as she can make, and her profit is P390 per floor lamp and P330 per table lamp. Identify the variables: Set up the objective function: Give the constraints in mathematical expression: Graph the constraints and identify the solution: How many floor lamps and how many table lamps should she make each week to maximize her weekly profit? What is the maximum profit per week?

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Transcript

00:01 In this problem, it is given that a crafts woman produces two products.

00:06 One is floor lamps denoted as f and the other is table lamps denoted as t.

00:12 And she takes 75 minutes to make one floor lamp while 50 minutes to make one table lamp.

00:22 And also the cost for producing one floor lamp is p -250 and that of one table lamp is p -200.

00:31 And also the person cannot spend more than 40 hours a week for the production and also cannot spend more than p -9 ,000 per week for the production cost.

00:53 And also the profit per item for selling the floor lamp is p -390 and that of the, the, table lamp is p 330.

01:10 The question is to determine the number of lamps of each type that must be produced in a week in order to maximize the profit.

01:21 So here this is this can be solved as a linear programming problem denoted as lpp.

01:28 And for that first we need to define variables for the problem.

01:32 The variables are the number of types of each lamp.

01:36 So let x denotes the number of floor lamps produced in a week and y denotes the number of table lamps produced in a week.

01:50 Next we need to define an objective function.

01:54 Now here the quantity that has to be maximized is profit.

02:01 So the objective function is the weekly profit function denoted as set and that is 390x plus 330 y.

02:12 Since the profit per item is known and the total number of items produced in a week is also known from which we can construct this objective function.

02:21 Now this is subject to certain constraints.

02:24 The first constraint is with respect to the time that can be totally spent in a week.

02:34 For production.

02:35 Now 40 hours corresponds to 2 ,400 minutes since one minute is 60 once hour is 60 minutes...

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