A company makes two types of calculators, one that uses batteries and one that is solar powered. The production of each battery operated calculator involves 1 hour on Machine A, 2 hours on Machine B, and 1 hour on Machine C. The production of each solar powered calculator involves 2 hours on Machine A, 1 hour on Machine B, and 1 hour on Machine C. The company can use Machine A for a total of 14 hours, Machine B for a total of 17 hours, and Machine C for a total of 9 hours. If the company can earn a profit of $2 for each battery powered calculator and $6 for each solar powered calculator, how many of each should it produce in order to maximize profit? What is the maximum profit it can earn?

A company makes two types of calculators, one that uses batteries and one that is solar powered. The production of each battery operated calculator involves 1 hour on Machine A, 2 hours on Machine B, and 1 hour on Machine C. The production of each solar powered calculator involves 2 hours on Machine A, 1 hour on Machine B, and 1 hour on Machine C. The company can use Machine A for a total of 14 hours, Machine B for a total of 17 hours, and Machine C for a total of 9 hours. If the company can earn a profit of $2 for each battery powered calculator and $6 for each solar powered calculator, how many of each should it produce in order to maximize profit? What is the maximum profit it can earn?

Name: A company makes two types of calculators, one that uses batteries and
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: A company makes two types of calculators, one that uses batteries and one that issolar powered. The production of each battery operated calculator involves 1 houron Machine A, 2 hours on Machine B, and 1 hour on Machine C. The production ofeach sola

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: A company produces two kinds of products. A product of the first type requires 3 hours of assembly…

A: Product (A) = X Market value = $21Assembly labour = 3 hours Testing = 3/2 hours Raw material = $2…

Q: A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will…

Q: 1. An energy company uses three different processes for generating electricity. One of the processes…

A: The energy company aims to optimize its electricity generation considering various processes with…

Q: In a certain factory, there are two tanks used to mix brine (also known as salt water). Tai 10…

Q: A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will…

A: Given that:A company wishes to produce two types of souvenirs Type-A and Type-B. Type-A…

Q: As a part of my 4H project, I took 100 bunnies and split them into two groups. One group I only fed…

Q: A refinery has two smelters that extract metallic iron ore. Smelter A pro- cesses 1000 tons of iron…

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: A factory manufactures chairs, tables and bookcases each requiring the use of three o utting,…

A: Let Chairs=x Tables=yBookcases=z

Q: An electronics company produces and 1 unit of glass. Each resistor these materials, respectively.…

A: Given data: Let x= units of copper y= units of zinc z= units of glass Rewriting given…

Q: Shop A provides 2 hours of cake training, 4 hours of cupcake training and 2 hours of bread training.…

A: To solve this problem, we can use linear programming. First, let's construct a table showing the…

Q: A researcher wants to provide a rabbit exactly 112 units of protein, 212 units of carbohydrates, and…

A: Given,protein=112 unitscarbohydrates= 212 unitsvitamin A= 50 units

Q: An angler fishes half of their time at East Delaney Lake, one quarter of their time at South Delaney…

A: It is given that in East Delaney Lake, 6% of the trout are brown trout, in South Delaney Lake 64% of…

Q: tables and chests. Producing a chair requires 2 hours of construction and 1 hour of painting.…

Q: Professor X spends his professional time among teaching, research, and committee meetings. None of…

A: He spends 3/5 of his teaching time in order to spend time for preparing to teach.3/5 of his teaching…

Q: A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will…

A: (a) To find the time available on Machine II for a meaningful solution, we need to set up the…

Q: Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux.…

Q: Jenck's Homemade Ice Cream, LLC is planning its production for next week. As there is a current…

A: We can formulate the problem as follows: Let x be the number of hundred-gallon units of chocolate…

Q: A company produces three types of bookcases: Standard, Deluxe, and Premium. Each bookcase must be…

Q: Mr.and Mrs. Jack Sear own and operate Electronics City, a small electronics store. Jack Sear worked…

A: In this question, we will examine the concept of capacity planning in the context of a small…

Topic Video

Question

A company makes two types of calculators, one that uses batteries and one that is
solar powered. The production of each battery operated calculator involves 1 hour
on Machine A, 2 hours on Machine B, and 1 hour on Machine C. The production of
each solar powered calculator involves 2 hours on Machine A, 1 hour on Machine B,
and 1 hour on Machine C. The company can use Machine A for a total of 14 hours,
Machine B for a total of 17 hours, and Machine C for a total of 9 hours. If the
company can earn a profit of $2 for each battery powered calculator and $6 for each
solar powered calculator, how many of each should it produce in order to maximize
profit? What is the maximum profit it can earn?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Optimization$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

A shoe company manufactures two types of shoes: tennis and basketball. Each shoe requires the use of two operations, stitching and coloring, and there are at most 28 hours available each day for each operation. A pair of tennis shoes requires 2 hours of stitching and 2 hours of coloring, while a pair of basketball shoes needs 1 hour of stitching and 2 hours of coloring. Due to other restrictions, the company can make at most 183 pairs of shoes a day. Additionally, due to a sponsorship agreement, the company needs to produce at least 4 pairs of tennis shoes for each pair of basketball shoes. The objective function is subject to constraints. Determine the constraints below. (Hint: Write the constraints line by line. Separate the non-negativity constraints with commas.)
Kane Manufacturing has a division that produces two models of grates, model A and model B. To produce each model A grate requires 3 pounds of cast iron and 6 minutes of labor. To produce each model B grate requires 4 pounds of cast iron and 3 minutes of labor. The profit for each model A grate is $1.75, and the profit for each model B grate is $1.25. Available for grate production each day are 1000 pounds of cast iron and 20 labor-hours. Because of an excess inventory of model A grates, management has decided to limit the production of model A grates to no more than 180 grates per day. Maximize P = 1.75x + 1.25y subject to 3x + 4y ≤ 1000 Resource 1 6x + 3y ≤ 1200 Resource 2 x ≤ 180 Resource 3 y ≥ 0 x ≥ 0 (a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.)$ (b) Identify the binding and nonbinding constraints. constraint 1 constraint 2 constraint 3
The firm WebsAreUs creates and maintains Web sites for client companies. There are two types of Web sites: “Hot” sites change their layout frequently but keep their content for long times; “cool” sites keep their layout for a while but frequently change their content. Maintaining a hot site requires 1.5 hours of layout time and 2 hour for content changes. Maintaining a cool site requires 1 hour of layout time and 2 hr for content changes. Everyday WebsAreUs has 12 hrs available for layout changes and 16 hr for content changes on a hot site. Net profit is $50 for a set of changes on a hot site and $250 for a set of changes on a cool site. To maximize profit, how many of each type of site should WebsAreUs maintain daily? How, if at all, do the maximum profit and optimal policy change if the company must maintain at least two hot and 3 cool sites daily?
A manufacturer of skis makes two types of skis: downhill and cross-country skis. The ski production process involves two steps: manufacturing and finishing. The manufacturing time is 3 hours per ski for downhill skis and 2 hours per ski for cross-country skis. The finishing time is 5 hours per ski for downhill skis and 2 hours per ski for cross-country skis. There are only 20 hours per week available for the manufacturing process and 25 hours for the finishing process. Due to existing sales contracts, at most 3 cross-country skis can be made for each downhill ski. The average profit is $43 for each downhill ski and $52 for cross-country ski. The manufacturer wants to know how many of each type of ski should be made to maximize the weekly profit. (a) Identify and clearly define the variables needed to solve the linear programming problem. x= y= P= (b) Find the objective function. Select whether it's maximizing or minimizing in the first answer blank and enter your…
Kane Manufacturing has a division that produces two models of grates, model A and model B. To produce each model A grate requires 3 pounds of cast iron and 6 minutes of labor. To produce each model B grate requires 4 pounds of cast iron and 3 minutes of labor. The profit for each model A grate is $2.00, and the profit for each model B grate is $1.50. Available for grate production each day are 1000 pounds of cast iron and 20 labor-hours. Because of an excess inventory of model A grates, management has decided to limit the production of model A grates to no more than 180 grates per day. Maximize P = 2x + 1.5y subject to 3x + 4y ≤ 1000 Resource 1 6x + 3y ≤ 1200 Resource 2 x ≤ 180 Resource 3 y ≥ 0 x ≥ 0 (a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.)$ (b) Identify the binding and nonbinding constraints. constraint 1 constraint 2 constraint 3
A certain drug is made from only two ingredients: compound A and compound B. There are 3 milliliters of compound A used for every 4 milliliters of compound B. If a chemist wants to make 567 milliliters of the drug, how many milliliters of compound A are needed?
XYZ Corporation operates two plants, each of which has a capacity of 200 units per day. Each day, XYZ must ship their product to each of four customers. Customers A, B, and C each have a demand of 17 units per day while customer D has a demand of 349 units per day. The cost of shipping one unit of each product from each of the two plants to each of the customers is shown in the table below. Customer A Customer B Customer C Customer D Plant 1 25 19 12 14 Plant 2 15 21 23 20 How many units should XYZ ship from each plant to each customer?
A tent manufacture produces regular and expedition tents at three branches. Per hour of operation, the Harrogate branch produces 20 regular tents and 10 expedition tents. The Skipton branch produces 0 regular tents and 20 expedition tents, and the York branc h produces 80 regular tents and 20 expedition tents. In order to meet the demand, the company needs to produce exactly 240 regular tents and 100 expedition tents each day. How many hours per day should each branch operate in order to produce the required amounts of tent? Solve using Gauss-Jordan elimination method.