A cobbler family makes mainly two types of shoes for Gents and Ladies. The Gents' shoe takes 1.5 hours of machining time and 3 hours of manual labour. For the Ladies' shoe it takes 3 hours of machining time and 1 hour of manual labour. Maximum machine-time available in a day is 42 hours and man-hours available is 24 hours. The profit on the Gents' shoe and Ladies' shoe are RO 6 and RO 3 respectively. Determine the number of shoes of each type that must be made so as to maximize the profit by optimizing the resources. What is the maximum profit that could be made?

A cobbler family makes mainly two types of shoes for Gents and Ladies. The Gents' shoe takes 1.5 hours of machining time and 3 hours of manual labour. For the Ladies' shoe it takes 3 hours of machining time and 1 hour of manual labour. Maximum machine-time available in a day is 42 hours and man-hours available is 24 hours. The profit on the Gents' shoe and Ladies' shoe are RO 6 and RO 3 respectively. Determine the number of shoes of each type that must be made so as to maximize the profit by optimizing the resources. What is the maximum profit that could be made?

Name: A cobbler family makes mainly two types of shoesfor Gents and Ladies.
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: A cobbler family makes mainly two types of shoesfor Gents and Ladies. The Gents' shoe takes 1.5hours of machining time and 3 hours of manuallabour. For the Ladies' shoe it takes 3 hours ofmachining time and 1 hour of manual labour.Maximum machine-ti

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: ROA Agri Feeds Corporation produces specially blended feed supplements. It has an order of 400…

A: We have to make 400 kilograms of the mixture using two kinds of ingredients such that it contains…

Q: The ABC Company manufactures two electrical products: air conditioners and water heaters. Each air…

A: Linear Programming: It is a technique of solving the problem and giving the optimizing solution that…

Q: 1. Kucci Sdn. Bhd. uses leather and synthetics rubber to produce two types of purse, Twilight and…

A: We will construct a linear programming problem according to the given conditions and solve it using…

Q: The average yearly salary of a woman with a bachelor’s degree exceeds that of a woman with an…

A: The provided statement is “The average yearly salary of a woman with a bachelor’s degree exceeds…

Q: A furniture company makes dining room furniture. A buffet requires 40hours for construction and 10…

A: A furniture company makes dining room furniture. A buffet requires 40 hours for construction and 10…

Q: A power plant burns coal, oil, and gas to generate electricity. Suppose that each ton of coal…

A: Consider the provided question, A power plant burns coal, oil, and gas to generate electricity.…

Q: Campustown Dry Cleaners has a variable demand. The daily demand ranges from 100 to 140 customers a…

Q: In a busy period, you are required to use the support of external agencies for 7 working days.…

A: To find out how much this will cost your department, we need to consider the day rates for each…

Q: A donut shop makes 2 kinds of donuts: fried and baked. Each donut requires flour, sugar, and time…

A: A) We will make a table of values. Flour (cups) Sugar (cups) Time (minutes) Price (dollars)…

Q: Some students want to start a business that cleans and polishes cars. It takes 2.5 hours of labor…

A: As this question is MCQ, it is easy enough with option-check. For cleaning they make $6.75/car For…

Q: The phones at Affordable Cellphones vary in price depending upon demand. The average flip phone has…

A: Just list out the given conditions and then create a quadratic equation using those conditions and…

Q: You are thinking of making your home more energy efficient by replacing some of the light bulbs with…

A: Given- You are thinking of making your home more energy efficient by replacing some of the light…

Q: Hours' constraint is: 2.5X1+1.5X2<150 2.5X1+1.5X2<120 2X1+1.5X2120 1.5X1+2.5X2<150

A: Given the students want to start a business that cleans and polishes car. Time taken to clean a car…

Q: A manufacturer of downhill and cross-country skis reports that manufacturing time is 1 hours and 4…

Q: Fixed costs=$85000, unit variable cost=$48, selling price per unit=$75. Find the break even number…

A: The formula for break even number in units is, Q=FCSP(per unit)-VC(per unit) Here, Q: break even…

Q: Some students want to start a business that cleans and polishes cars. It takes 2.5 hours of labor…

A: The linear function(cost function or the profit function etc.) that needs to be optimized(maximize…

Q: Cost' constraint is: * 1.5X1+2.5X2S150 3X1+1.5X2<120 2.5X1+1.5X2<150 O 1.5X1+3X2<120 O O O O

Q: A craftsman produces two products: floor lamps and table lamps. Production of one floor lamp…

A: labor material cost profit Floor lamps 70 210 395 table Lamps 50 190 345 availability 40…

Q: You are thinking of making your home more energy efficient by replacing some of the light bulbs with…

A: Given- You are thinking of making your home more energy efficient by replacing some of the light…

Q: The ABC Company manufactures two electrical products: air conditioners and water heaters. Each air…

A: Tabulate the given information, to formulate it as a linear programming problem. Profit 25 15…

Q: Sweet-Fit jeans has a factory that makes two styles of jeans; Super-Fit and Super-Hug. Each pair of…

A: Given: The factory makes two styles of jeans: Super-Fit and Super-Hug. It takes 18 minutes to cut…

Q: Apple Inc. has a demand for its Iphone 8 and Iphone 8s phones in the Philippines for the 4th Quarter…

A: Let the units of iPhone 8 to be produced be x and the units of iPhone 8s to be produced be y. We are…

Q: A nut packager has on hand 100 kg of peanuts, 50 kg of cashew nuts and 70 kg macademian nuts. He can…

A: Linear programming is the mathematical program to achieve the optimal solution for a given objective…

Q: A company manufactures two types of washers, top load and front load. The company can manufacture a…

A: Let us assume they will make x top load and y front load washing machines. According to the…

Q: Wetlands offer a diversity of benefits. They provide a habitat for wildite, spawning grounds for…

A: Given data : 9, 20, 24, 27, 30, 33, 35, 35, 35, 37, 38, 42, 45, 45, 45, 48, 50, 50, 51, 51, 55, 59,…

Q: A company that makes wooden tables and chairs has its production process with two basic types of…

A: It is provided that the item T requires 2 hours of carpentry and 1 hour of finishing. It is provided…

Topic Video

Question

A cobbler family makes mainly two types of shoes
for Gents and Ladies. The Gents' shoe takes 1.5
hours of machining time and 3 hours of manual
labour. For the Ladies' shoe it takes 3 hours of
machining time and 1 hour of manual labour.
Maximum machine-time available in a day is 42
hours and man-hours available is 24 hours. The
profit on the Gents' shoe and Ladies' shoe are RO
6 and RO 3 respectively. Determine the number of
shoes of each type that must be made so as to
maximize the profit by optimizing the resources.
What is the maximum profit that could be made?

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps with 1 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

Some students want to start a business that cleans and polishes cars. It takes 2.5 hours of labor and costs $1.5 in supplies to clean a car. It takes 1.5 hours of labor and costs $3 in supplies to polish a car. The students can work a total of 150 hours in one week. They also decide that they want to spend no more than $120 per week on supplies. The students expect to make a profit of $6.75 for each car that they clean and a profit of $9.50 for each car that they polish. Hours’ constraint is: * 2.5X1+1.5X2≤150 2.5X1+1.5X2≤120 2X1+1.5X2≤120 1.5X1+2.5X2≤150
Blackjack Company is a local producer of Black shampoo. The company wants to determine the production mix that will yield the maximum profit. The production process takes 5 minutes to mix 1 case of men's shampoo and 10 minutes to mix 1 case of women's shampoo. This process is done for 100 minutes per day. It takes 7 minutes to bottle 1 case of men's shampoo and 7 minutes to bottle 1 case of women's shampoo. Eighty four minutes is consumed for the bottling process per day. It takes 9 minutes to pack 1 case of men's shampoo anf 5 minutes to pack 1 case of women's shampoo. The total number of minutes available for the packing process is 90 minutes. The company earns P60 for every case of men's shampoo and P80 for women's shampoo. You are required to peform these steps: Tabulate the data and statement variables. Formulate the objective function and constraints. Graph the objective functions by first converting the inequalities into equations. Then, find their intercepts.…
Find the final amount of money in an account if $8,100 is deposited at 6.5% interest compounded quarterly every 3 months and the money is left for 5 years
A toy factory creates miniature steel train engines and box cars. The fabrication department has 5,279 minutes available per week and the assembly and finishing department has 5,999 minutes available per week. Manufacturing one miniature steel train engine requires 12 minutes of fabrication and 10 minutes of assembling and finishing. Manufacturing one miniature steel box car requires 6 minutes of fabrication and 10 minutes of assembling and finishing. The profit on each miniature steel train engine is $9.50 and the profit on each miniature steel box car is $8.25. How many steel train engines and steel box cars should be produced each week to obtain the maximum profit? Find the maximum weekly profit. (Use x for box car and y for train engine.) Maximize P = ≤5, 279 5,999 subject to Enter the solution to the simplex matrix below. If there is no solution enter 'DNE' in the boxes below. If more than one solution exists, enter only one of the multiple solutions below. If needed round toys to…
Sweet-Fit jeans has a factory that makes two styles of jeans; Super-Fit and Super-Hug. Each pair of Super-Fit takes 14 minutes to cut and 15 minutes to sew and finish. Each pair of Super-Hug takes 14 minutes to cut and 35 minutes to sew and finish. The plant has enough workers to provide at most 13,999 minutes per day for cutting and at most 25,999 minutes per day for sewing and finishing. The profit on each pair of Super-Fit is $4.00 and the profit on each pair of Super-Hug is $5.00. How many pairs of each style should be produced per day to obtain maximum profit? Find the maximum daily profit. (Use for Super-Fit and y for Super-Hug.) Maximize P = 4.00x + 5.00y subject to 14x + 14y 13, 999 15x + 35y 25, 999 Enter the solution to the simplex matrix below. If there is no solution enter 'DNE' in the boxes below. If more than one solution exists, enter only one of the multiple solutions below. If needed round jeans to 1 decimal place and profit to 2 decimal places. Number of Super-Fit…
Happy Kid Toy Company produces two types of toy cars, A and B. The company makes RM 50 profit for each toy car of type A and RM 30 profit for each toy car of type B. It takes 4 hours to produce the parts of one unit of A, 2.5 hours to assemble and 1.5 hours to paint. It takes 2 hours to produce the parts of one unit of B, 1 hour to assemble and 2 hours to paint. Every month, 2000 hours are available for pruducing the parts, 1800 hvurs for assembling the parts and 1550 hours for painting the toy cars. The company wishes to determine the best possible combination of toy cars A and B to be produced monthly to maximise the total profit. (i) Formulate the above as a linear programming problem. (ii) Solve the problem graphically. Obtain the optimal product mix and calculate the maximum total profit. (iii) By how much could the unit profit of toy car B change before the optimal product mix could change?
please answer this question asap thank you.
Rey is choosing a profession in engineering. He is choosing between civil, chemical and mechanical engineering. He searched about the annual income of each engineering profession and wants to consider this when choosing. An Civil Engineer earns an average of 196,000 per year with a tax rate of 25%, a Chemical Engineer earns an average of 221,000 a year with a tax rate of 25%, and lastly, Mechanical Engineer earns an average of 587,000 a year with a tax rate of 32%, which among this profession should he choose if he will consider the net income?
PLEASE ANSWER EVERYTHING. I WILL UPVOTE ALL I PROMISE.
A toy factory creates miniature steel train engines and box cars. The fabrication department has 3,679 minutes available per week and the assembly and finishing department has 3,099 minutes available per week. Manufacturing one miniature steel train engine requires 8 minutes of fabrication and 5 minutes of assembling and finishing. Manufacturing one miniature steel box car requires 4 minutes of fabrication and 5 minutes of assembling and finishing. The profit on each miniature steel train engine is $8.00 and the profit on each miniature steel box car is $7.25. How many steel train engines and steel box cars should be produced each week to obtain the maximum profit? Find the maximum weekly profit. (Use x for box car and y for train engine.) Maximize P subject to %3D < 3, 679 < 3, 099 Enter the solution to the simplex matrix below. If there is no solution enter 'DNE' in the boxes below. If more than one solution exists, enter only one of the multiple solutions below. If needed round toys…
ou are thinking of making your home more energy efficient by replacing some of the light bulbs with compact fluorescent bulbs and insulating part or all of your exterior walls. Each compact fluorescent light bulb costs $4 and saves you an average of $2 per year in energy costs, and each square foot of wall insulation costs $1 and saves you an average of $0.20 per year in energy costs.+ Your home has 40 light fittings and 1,300 square feet of uninsulated exterior wall. You can spend no more than $1,400 and would like to save as much per year in energy costs as possible. How many compact fluorescent light bulbs and how many square feet of insulation should you purchase? (If an answer does not exist, enter DNE.) compact fluorescent light bulbs
Martin Company has a current breakeven point of 47,000 units. To reduce the breakeven point, Martin should increase the contribution margin per unit. increase variable costs. reduce the contribution margin per unit. reduce the sales price per unit.