Question: Consider a rectangle in the xy-plane, with corners at (0, 0), (a, 0), (0, b), and (a, b). If (a, b) lies on the graph

Consider a rectangle in the xy-plane, with corners at (0, 0), (a, 0), (0, b), and (a, b). If (a, b) lies on the graph of the equation y = 30 - x, find a and b such that the area of the rectangle is maximized. What economic interpretations can be given to your answer if the equation y = 30 - x represents a demand curve and y is the price corresponding to the demand x?

Step by Step Solution

★★★★★

3.36 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The objective is A xy and the constraint is The maximum value of Ax oc... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Applied Calculus Questions!

A rectangular loop in the xy plane with sides b (6 m) and b (7 m) carrying a current of 2 A lies in a uniform magnetic field B = 3 ax + 4 ay + 5 az. Determine the force on the loop. 1022 F = F = F3 =...

A circular ring of charge of radius a lies in the xy plane and is centered at the origin. If the ring is in air and carries a uniform density l , (a) Show that the electrical potential at (0,...

At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of vi = (3.00i 2.00j) m/s and is at the origin. At t = 3.00 s, the particles velocity is v = (9.00i + 7.00j) m/s....

\"mu\" 7 Consider the vector field Tries. . th, y, 2] = (6X, 57n 9y): remaining: 3 Marked out of 1 _ In no Evaluate the line integral [E F - air, where C is the intersection curve of the paraboloid...

Question 8 Let S be the surface in R3 that lies on Tries _ 3 _ 2 remainingla C _ {(xhy'Z) ER I z_x +3y} Marked 0'41 0' and above the triangle in the xy-plane with corners (0. 0), (2, 0). (2.5). Then...

The University of Sydney School of Mathematics and Statistics Vector Calculus Assignment MATH2061/2067: Vector Calculus Semester 1, 2017 This assignment is due by Friday 26 May 2017 at 4:00pm and is...

\f1.0 0.75 2 0.5 0.25 O 1 0.0 anewHHHH X 2 1 2 y 3 3 Note: The graph is an example. The scale may not be the same for your particular problem.Let E be the region bounded above by a2 + y" + 2" =102 ,...

Consider a square in the xyplane. The corners of the square are located at (1, 1, 0), (1, -1, 0), (-1, -1, 0) and (-i, 1, 0). The surface charge density e, within the square is 1.7265 x 10-10x[x + y...

Consider the equation f(x) = cos(x) - ln(x) + ex^2 that exists over the interval x elementof [0, pi]. For our purposes, we hope to plot f(x) vs. x in 4 different ways. Create a figure containing a 2...

The light vehicle market share in percent in a particular country for pickup trucks is shown in the graph Let x 0 represent 1995 x 4 represent 1999 and so on a Use the points on the graph to write...

Are any of the gurus quality contributions used where you work or have worked? Explain how.

A body of mass 5 kg is placed at the origin, and can move only on the x-axis. A force of 10N is acting on it in a direction making an angle of 60 with the x-axis and displaces it along the x-axis by...

According to the economic theory of labor markets, if unions are successful in raising wages, with no accompanying increase in labor productivity, then which of the following is true? a. The quantity...

6. Why are the current assets always listed in the same order?

Compute the standard deviation based on the sample of six means. What is another name for this quantity? Table 6.2: Sample of birth-weights (oz) obtained from 1000 consecutive deliveries at Boston...

Select the third point from each of the six samples, and compute the sample sd from the collection of six third points? Table 6.2: Sample of birth-weights (oz) obtained from 1000 consecutive...

What theoretical relationship should there be between the standard deviation in Problem 6.48 and the standard deviation in Problem 6.49? Table 6.2: Sample of birth-weights (oz) obtained from 1000...

The spot rate and the 90-day forward rate on the South African rand are 7.7754 and 7.8795 respectively. Is the dollar at a forward discount or premium on the rand? - Forward discount - Forward...

#1 Finance knowledge is crucial for an entrepreneur launching a startup to create a viable business plan, secure funding, and manage cash flow effectively. Finance knowledge is crucial for an...

What is theoretically the highest possible EAR given an APR of 31%? Hint: Think about compounding/discounting periods in time value of money; when you compound/discount more times during a year, does...