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?

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?

Name: Happy Kid Toy Company produces two types of toy cars, A and B. The co
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: Happy Kid Toy Company produces two types of toy cars, A and B. The company makesRM 50 profit for each toy car of type A and RM 30 profit for each toy car of type B. It takes 4hours to produce the parts of one unit of A, 2.5 hours to assemble and 1.5

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: The campus store sells dessert, Sobolo drink and Brukina drink. The Sobolo cost GH₵1.90 and the…

A: Cost of Sobolo drink is GH₵1.90 and and Brukina drink cost is GH₵2.25. Selling price is Sobolo drink…

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: If Sandy can paint a fence in 2 hours and Erik can paint the fence in 3 hours, if they work…

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: Peter has some candies. He places 2/3 of his candies equally into 12 small boxes, and the rest…

A: Let Peter have x candies in total.

Q: Suppose Ahmed can mow a yard in 4 hours. If he keeps a steady pace, in 1 hour he would finish of the…

A: First, we need to identify the rate of work for each person. The rate of work is defined as the…

Q: A furniture company makes dining room furniture. A buffet requires 30 hours for construction and 10…

Q: • What restriction (on x or y) does dy have? What dx point (x, y) does this correspond to? • Find…

A: According to our policies we are allowed to answer only one question at a time. If you want solution…

Q: Because of new federal regulations on pollution, a chemical plant introduced a new, more expensive…

A: The older process emitted 8 grams of sulfur dioxide and 24 grams of particulate matter into the…

Q: If a bathtub comfortably holds 30 gallons of water and a shower produces 2 gallons of water per…

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: A baker has 30 oz of flour and 5 packages of yeast. Baking a loaf of bread requires 5 ozof flour and…

A: Given: Amount of flour = 30 oz. Amount of yeast = 5 packages. Baking a loaf of bread requires 5 oz…

Q: There are 3 types of boilers in a glove company, namely boiler A, B and C. The utility cost per hour…

Q: The JAV Company manufactures two types of lamps; Special lamp and regular lamp. Each special lamp…

A: Given: Let's take x and y to be the production quantities of special lamps and regular lamps. Now…

Q: A chef purchases whole chickens because they cost less per pound than fabricated cuts and the…

Q: The company is engaged in the handmade production of furniture. Its main products are chairs, dining…

A: We need to form three linear equation with three variable and then need to solve it

Q: When Josh and Sean were each 5 years old, Josh was 1.5 inches taller than Sean. Josh grew at an…

A: Josh is 1.5 inches taller than Sean at the age of 5 year of each, at the age of 13 height of Josh…

Q: A population gathers plants and animals for survival. They need at least 440 units f energy, 300…

Q: A bacteria culture initially contains 2000 bacteria and doubles every half hour. Find the size of…

Q: Suppose a total of 15 ounces of medicine is added to the original mixture (so that the total volume…

Q: The time required to process a shipment of oysters varies directly with the number of pounds in the…

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

Topic Video

Question

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?

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

VIEW

Step 2

VIEW

Step 2

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Application of Algebra$

Learn more about

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

Similar questions

Farmer Roy raises sheep and cows. He has 1000 acres available to pasture them. Each sheep requires half an acre of pasturage. Each cow requires two acres of pasturage. Farmer Roy has 28 thousand square feet of barn space for sheltering the animals. Cows each require 50 square feet of space. Sheep require 15 square feet. If Farmer Roy can earn \$100 profit per sheep and \$375 per cow, how many of each should he have? COWS sheep If you are having any trouble getting the above points for this question, please submit what you are using for objective function and constraints and I will check them. Otherwise, just type "I'm good." in the essay box. I
A robot manufacturer must produce a total of 1260 robots in one week, including both “building robots”and “destroying robots.” The number of building robots needs to be 3.5 times the number of destroyingrobots. How many of each should they make?
A company produces widgets at plants 1 and 2. It costs 125x1y2 dollars to produce x units at plant 1 and 235x1y3 dollars to produce x units at plant 2.Each plant can produce up to 500 units. Each unit produced can be sold for $10. At most 800 widgets can be sold. Determine how -the company canmaximize its profit.
Two classmates have decided to read all the volumes in a popular series of books. Mia has already read 12 volumes and will continue to read new ones at a rate of 1 volume per week. Beth, who hasn't started reading the series yet, will read 4 volumes per week. At some point, Beth will catch up with Mia and they will be reading the same book. How long will that take? How many volumes will each girl have read by then? In ? weeks, the girls will each have read ? volumes in the series.
Mr. Saleh is one of the school canteen operators who joined The Supplementary Food Plan (RMT) organized by the Ministry of Education Malaysia. Assuming that each RMT student has been allocated RM3-RM4 for his meal per day. Due to that, Mr. Saleh needs to prepare one meal set consisting of one chicken rice and a box of milk for each RMT student. The raw cost of one week of meal preparation for 20 RMT students is as much as RM330 while for 100 RMT students are RM1650. The cost of chicken rice is twice the cost of the milk. Write simultaneous equations for the above situation. а. b. With the substitution method, determine the cost for chicken rice. с. With the elimination method, find the cost of each milk. d. Determine the raw cost of each RMT meal. Calculate the maximum number of RMT students that can be allocated if the weekly budget is RM2500. е.
Bottled water and medical supplies are to be shipped to survivors ofan earthquake by plane. Each container of bottled water will serve 10 people and eachmedical kit will aid 6 people. Each plane can carry no more than 80,000 pounds. The bottledwater weighs 20 pounds per container and each medical kit weighs 10 pounds. Each planecan carry a total volume of supplies that does not exceed 6000 cubic feet. Each waterbottle is 1 cubic foot and each medical kit also has a volume of 1 cubic foot. Thus, the maximum value of z is 36000 and this occurs when x = 0and y = 6000.In practical terms, this means that the maximum number of earthquake survivors whocan be helped with each plane shipment is 36000. This can be accomplished bysending 6000 medical kits.A) TrueB) False
The workers of the company "Malova" work in a 5-day work week and worked them for 22 days in the month of November 2020. The standard work schedule is 8 hours per day with a 30-minute break included in this time. Now, "Malova's" company is in the process of manufacturing screwdrivers and manufactured 3100 pieces of screwdrivers. In addition, the company manufactures screwdrivers in batches of 300 and after each batch makes a pause to check the quality of production and make certain adjustments to the machines if necessary. The break is 1 hour. Calculate the parts produced per hour by the Malova company in November. Important: Use the formula (the one I put in the image)
You are designing a poster which has a border around the printed portion. The border is 2 inches wide on the left and right sides, and 3 inches wide on the top and bottom. The entire poster will be a total of 300 square inches, including the borders and printed portion combined.
Arrange these steps in the correct order to prove that if you have an 8-gallon jug of water and two empty jugs with capacities of 5 gallons and 3 gallons, respectively, then you can measure 4 gallons by successively pouring some of or all of the water in a jug into another jug in the correct order. Rank the options below. Fill the 3-gallon jug from the 5-gallon jug, leaving (3, 2, 3). Empty the 5-gallon jug's contents into the 3-gallon jug, leaving (6, 0, 2), and then fill the 5-gallon jug from the 8-gallon jug, producing (1, 5, 2). Fill the 5-gallon jug from the 8-gallon jug, leaving the contents (3, 5, 0), where the ordered triple is used to record the amount of water in the 8-gallon jug, the 5-gallon jug, and the 3-gallon jug, respectively. Top off the 3-gallon jug from the 5-gallon jug, and there will be (1, 4, 3), with four gallons in the 5-gallon jug. Pour the contents of the 3-gallon jug back into the 8-gallon jug, leaving (6, 2, 0). ❤ ← ←