1.A department store has found that its value of sales (z) depends on the number ofadvertisements in circulars (x) and in newspapers (y), given byz = 420x – 2x2 – 3xy – 5y? + 640y + 1725.If the price per advertisement is RM1 in circulars and RM4 in newspapers, andthe advertising budget is RM180,iii)Use the Bordered Hessian to show that the sales are in fact a maximum.iv)Estimate the effect on sales of a $1 increase in the advertising budget. Provideyour comment.

Note:- $1=4.17 RM From Part (i), we have The problem is maximum z=420x-2x2-3xy-5y2+640y+1725subject…

Answered: 1. A department store has found that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The line given by the equation y = x is shifted down 5 units and stretched vertically by a factor of 4, what is the equation of the new line? A. y=5x+4 B. y=1/4x+5 C. y=4x-5 D. y=-4x+5
Suppose that for a company manufacturing calculators, the cost, revenue, and profit equations are given by x² C = 90,000 + 20x, R=200x - A) Costs are increasing at the rate of $ (Simplify your answer.) where the production output in 1 week is x calculators. If production is increasing at a rate of 400 calculators per week when production output is 5,000 calculators. Find the rate of increase (decrease) in cost, revenue, and profit. B) Revenue is (Simplify your answer. C) Profits are (Simplify your answer.) at the rate of $ 20 at the rate of $ P=R-C per week at this production level. per week at this production level. per week at this production level.
If a company A manufactures t-shirts and sells them to retailers for $9.80 each. It has fixed cost of $2625 related to the production of the t-shirts and production cost per unit is $2.30. Company B also manufactures t-shirts and sell them directly to consumers. The demand for this product is p= 15-x/125, its production cost per unit is $5.00 and its fixed cost is the same as company A. 1. Derive the total revenue function, R(x) for company B. 2. Derive the profit function, for company B. 3. How many t- shirts should company B sell to in order to break even. 4. How many t- shirts must company B sell to maximise its profit.
A production process varies only with raw materials, as all other inputs are fixed.The cost of a shipment of 16kg of raw materials is fixed at $85.It takes 10kg of raw materials to create one item of output, Q.The marginal revenue for this production process is expressed by: MR = −Q^2 + 52Q − 576.Determine the optimal amount of raw materials to be used in this production process.
What is Power and Multiple Rules?
Solve. 7. 8. (answers attached)
The purchase price of a home y (in $1000) can be approximated based on the annual income of the buyer x1 (in $1000) and on the square footage of the home x2 (in 100 ft2) according to y = ax1 + bx2 + c. The table gives the incomes of three buyers, the square footages of the home purchased, and the corresponding purchase prices of the home. Square Footage (100 ft’) x2 Income Price ($1000) x1 ($1000) y 80 21 180 150 28 250 75 18 160 a. Use the data to write a system of linear equations to solve for a, b, and c. b. Use a graphing utility to find the reduced row-echelon form of the augmented matrix. c. Write the model y = ax1 + bx2 + c. d. Predict the purchase price for a buyer who makes $100,000 per year and wants a 2500 ft2 home.

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