5. A firm orders 12, 30 and 25 items of goods G1, G2 and G3. The cost of each item of G1, G2 and G3 is $8, $30 and $15, respectively. (a) Write down suitable price and quantity vectors, and use matrix multiplication to work out the total cost of the order. (b) Write down the new price vector when the cost of G1 rises by 20%, the cost of G2 falls by 10% and the cost of G3 is unaltered. Use matrix multiplication to work out the new cost of the order and hence find the overall percentage change in total cost.

5. A firm orders 12, 30 and 25 items of goods G1, G2 and G3. The cost of each item of G1, G2 and G3 is $8, $30 and $15, respectively. (a) Write down suitable price and quantity vectors, and use matrix multiplication to work out the total cost of the order. (b) Write down the new price vector when the cost of G1 rises by 20%, the cost of G2 falls by 10% and the cost of G3 is unaltered. Use matrix multiplication to work out the new cost of the order and hence find the overall percentage change in total cost.

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: company. b. Determine the dual price of the raw material resource and its allowable range. If…

Q: A corporation has three factories, each of which manufactures acoustic guitars and electric guitars.…

Q: 4. An automobile company uses three types of Steel S₁, S₂ and S3 for providing three different types…

Q: (c) A company manufactures two products: X and Y. Product X costs $8 per unit and contains 2 units…

Q: The downtowm core of Gotham City consists of one-way streets, and the traf- fic flow has been…

Q: Wilderness Fanatic, a manufacturer of outdoor goods, is willing to supply 1100 of its Blue Thrash…

Q: The inventory manager at a warehouse distributor wants to predict inventory cost (Cost in $) based…

A: We are given the costs and order quantities for the past 36 months. Now we will do further…

Q: 1. A manufacturing business can supply 60 plasma TV sets per month at a price of $280 per set, or…

A: Consider the equation

Q: 1. A wholesale buyer deals in only two items-Toffees and Wafers. He has 30,000 OMR to invest and has…

A: Let he buy x1 volume of Toffee boxes and x2 volume of water boxes.Max z=250x1+570x2Subject…

Q: It is estimated that 60% of emails are spam emails. Some software has been applied to filter these…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: In Nyameba Limited factory, inputs are important in producing products. One of the processing lines…

A: Given Information : In the Nyameba Limited factory, inputs are important in producing products.…

Q: In its average daily food consumption, a predatory animal needs 10 units of nutrient A, 12 units of…

A: Given information:Predator's daily nutrient requirements: of A, of B, and of C.Species I supplies:…

Q: Bruce and Cruz had 294 bookmarks altogether. Bruce gave away 3/8 of his bookmarks and Cruz gave away…

A: Let the number of bookmarks Bruce has = B The number of bookmarks Cruz has = C therefore B+C=294…

Q: Product Blend Example • Petroleum Mix Inputs Maximum Barrels Available/Day 4,500 2,700 3,500…

Q: 10. A farmer in Wood County has 900 acres of land. She is going to plant each acre with corn,…

Q: A store has two types of animal feed available. Type A contains 2 pounds of oats and 5 pounds of…

A: Type-A Type-B Requirement Oats 2 7 70 Corn 5 3 75 Store Capacity 30 20

Q: Mudassir Hussain, a PhD scholar at National University of Austria, need to make phone calls within…

A: Given that call rates are as x1 represents the rate for calls within Canada x2 represents the rate…

Q: A diet is to contain at least 845 units of carbohydrates, 1280 units of proteins, and 1010 calories.…

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

Q: Suppose an economy consists of three sectors: Energy (E), Manufacturing (M), and Agriculture (A).…

Q: A produce grower is purchasing fertilizer containing 3 nutrients: A, B and C. The minimum weekly…

A: (a) Write down the LP Model. In Blend 1,the number of units of the nutrient of A is 2n .In Blend…

Q: A farmer has 1100 acres of land and plans to plant corn and soybeans. The input cost (cost of seed,…

A: Let,the farmer plans to plant to maximize the profit in total under given constrants.then as per…

Q: A mining company owns two mines. These mines produce an ore that can be graded into two classes:…

A: First mine Second mine Minimum productionRegular grade coalLow grade coalMaximum operation time…

Q: 4. Let 0 ‡ b, c E Rn and define A = be E Rnxn. Show that (a) R(A) = span{b}, (b) N(A) = {x ≤ R" |…

A: (a) We are given that A = bcT where, c ∈ Rn So, R(A) = { Ax : x ∈ Rn×1 }…

Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

5. A firm orders 12, 30 and 25 items of goods G1, G2 and G3. The cost of each item of
G1, G2 and G3 is $8, $30 and $15, respectively.
(a) Write down suitable price and quantity vectors, and use matrix multiplication to
work out the total cost of the order.
(b) Write down the new price vector when the cost of G1 rises by 20%, the cost of G2
falls by 10% and the cost of G3 is unaltered. Use matrix multiplication to work out
the new cost of the order and hence find the overall percentage change in total cost.

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Matrix Operations$

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

need comprehensive and correct answers.This question is about optimization.
Write the above transportation problem as a LPP and Solve the LPP using graphical method
USE A,B,C=200
Two departments of a firm, A and B, need differing amounts of steel, wood, and plastic. The table on the right gives the amount of each product the departments need. These three products are supplied by two suppliers, Company C and Company D, with the unit prices given in the table on the right. a. Use matrix multiplication to determine how much these orders will cost each department at each of the two suppliers. Enter the amounts into the cost matrix shown on the right. Department A Department B Steel Wood Plastic Dept. A Dept. B Company C 600 310 310 Co. C Steel Wood Plastic 60 40 40 60 70 60 Company D 560 190 390 Co. D
A mining company owns two mines. These mines produce an ore that can be graded into two classes: regular grade and low grade. The company must produce at least 420 tons of regular - grade and 520 tons of low-grade ore per week. The first mine produces 6 tons of regular - grade and 18 tons of low-grade ore per hour. The second mine produces 18 tons of regular - grade and 9 tons of low-grade ore per hour. The operating cost of the first mine is $7000 per hour, and the operating cost of the second mine is $ 22,000 per hour. The first mine can be operated no more than 37 hours a week, and the second mine can be operated no more than 28 hours a week. How many hours per week should each mine be operated to minimize the cost?
A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r units of chemical R, where: z = 100p-75,0.25 Chemical P costs $100 a unit and chemical R costs $700 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $112,000. A) How many units each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint? Units of chemical P, p = Units of chemical R, r = B) What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production, z= units
ONLY ANSWER B3!!! The inventory manager at a warehouse distributor wants to predict inventory cost (Cost in $) based on order quantity (Quantity in units). She thinks it may be a nonlinear relationship because its two primary components move in opposite directions: (1) order processing cost (costs of procurement personnel, shipping, transportation), which decreases as order quantity increases (due to fewer orders needed), and (2) holding cost (costs of capital, facility, warehouse personnel, equipment), which increases as order quantity increases (due to more inventory held). She has collected monthly inventory costs and order quantities for the past 36 months. A portion of the data is shown in the accompanying table. Cost Quantity 54.4 844 52.1 503 60.2 300 53.8 869 51.7 525 57.1 1030 61.1 288 49.8 577 53.9 490 48.2 588 47.5 606 57.4 325 59.6 1160 58.2 1072 58.7 308 58.1 1140 48.4 627 63.4 214 62.5 207 62.5 1174 62.7 1190 61.2 1166…
Exercise 2. The demand per week for a book is 120 copies when the price is $8 each and 80 copies when the price is $10 each. a) Find the demand equation for the book, assuming that it is linear. b) Find the quantity demanded when the price is $13 each. c) Find the price if the quantity demanded id 2 books.
A company produces a special new type of TV. The company has fixed costs of $492,000, and it costs $1000 to produce each TV. The company projects that if it charges a price of $2300 for the TV, it will be able to sell 750 TVs. If the company wants to sell 800 TVs, however, it must lower the price to $2000. Assume a linear demand. How many TVs must the company sell to earn $1,925,000 in revenue? It needs to sell enter your response here TVs. (Round answer to nearest integer. If more than one answer, separate with a comma.)