Provide step by step solution with calculations for only task number 4 Variant 4 (extra).1. Find the partial derivatives of:=(x,y)=9sin.x-5x²y³ +7+ ycosx+e³2.Given z(x, y) = x².3√/y+ex-y +. find53. Find the local extrema of the given functionz(x,y)= x³ - 8y³ -12xy + 180³ =ôxôy?4.Boxowitz, Inc., a computer firm, markets two kinds of calculatorsthat compete with one another. Their demand functions are expressed by thefollowing relationships:91 = 64 4p1 - 2P2and92 56 2p1 - 4P2.where p₁ and p2 are the prices of the calculators, in multiples of $10 (thisinformation can be skipped, it is needed only to the answer), and q1 and q2 are thequantities of the calculators demanded, in hundreds of units. What prices p₁ andp2 should be charged for each product in order to maximize total revenue? Whatis the maximum total revenue?5. The golf ball manufacturer, Pro-T, has developed a profit model thatdepends on the number x of golf balls sold per month (measured in thousands),and the number of hours per month of advertising y, according to the functionP= f(x, y) = 48x +96y-x² - 2xy - 9y²,where P is measured in thousands of dollars. The budgetary constraint functionrelating the cost of the production of thousands golf balls and advertising unitsis given by 20x + 4y = 216. Find the values of x and y that maximize profit, andfind the maximum profit.

Total revenue means the overall income generated by a firm from the sale of its goods or services.…

Answered: 4. Boxowitz, Inc., a computer firm,…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Differentiate the function. dy dx y= || 6 X 30
Calculate the percentage change of the variable in each of the following cases. Then calculate the percentage change if the movement is occurring in the opposite direction, with what was the final value now the initial value and vice versa. Now calculate a comparable percentage change using the average of the initial and ending values. Express all three changes in absolute value form without positive or negative signs and as whole numbers (i.e. 67%, not 66.6%). a. A fast-food restaurant, which originally sold hamburgers at a price of $5, increases their price to $6. The absolute value of this percentage change is %, and the absolute value of the percentage change calculated using the average of the two values is %, the absolute value of the percentage change in the opposite direction is %. b. The number of autos sold monthly at a car dealership drops from 400 to 300. The absolute value of this percentage change is %, the absolute value of the percentage change in the opposite direction…
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(1) A course repeater claims that his brother who did some Calculus at college years ago, but currently on some cough medication, believes that the first derivative of (2x² – 1)(x² + 3) [(2x? – 1)(x² + 3) 2х + |2x2 -1 х2 +3 4x 2x | f(x) -is f'(x) x? + 1 x2 + 1] x2 + 1 and (x² + 8)7 14х (x2 + 8)7 30х + 2 – 3x2] |(2 – 3x²)5 that the first derivative of g(x) is g'(x) = (2 — Зx?)5 lx² + 8 ' Using the product, qoutient and chain rules you learnt in Unit 7 of this Course, could you confirm whether his brother is right, wrong or a little tipsy.
As the selling price of a product increases, demand decreases. Fewer people will buy a product if it is more expensive. This is a very important concept. The demand equation for new iSmarts is given by 0.025x , where p is the unit p = 100 price (in dollars) of the iSmart and x is the number of units produced. We can determine the total revenue (money earned for selling x iSmarts) by multiplying the number of items we sell, x and the price p. The total revenue obtained by producing and selling x iSmarts is given by = xp 100x – 0.025x². It makes sense that this function is quadratic. The company can price the iSmarts so high that no one will buy them and the revenue will be zero. The can also set the price to $0, but the revenue will still be $0, no matter how many iSmarts they "sell". In between, the graph is a parabola opening downward. Determine prices p that would keep revenue above 6530 dollars. Give your answers to 2 decimal places. The revenue will be above 6530 if price is…
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