ll T-Mobile8:25 PM96%Section 23 - Exercises (answers follow)e numbers z and y such that z +y 150 and zy is maximizedsu1. Find non-negative2. You are to enclose a rectangular garden having an area of 3,600square meters and surroundit by a fence. How can this be done using the least amount of fencing?3. What are the dimensions of an open (no top) rectangular box that has a square base, acapacity of 32,000cm3, and is constructed using the least amount of material?4. If a manufacturer charges p(x) dollars per item, where p(r) = 4-121 thenthousand itewill be sold(a) Find an expression for the total revenue from the sale of x thousand items(b) Find the value of z that leads to maximum revenue.(c) Find the maximum revenue.oduction of widgets the marginal revenue and marginal cost (in thousands of dollars+ 10per item) for producing z widgets are given by R()70-z and ()0.122 +4(a) What is the number x at which these are equal?(b) Interpret the result: for what value of x is profit maximal?6. Ifx units are produced, the cost of production is C(z)400 + 2x+ 0.05x2. In order tosel units it is known that the price per unit should be p(x)production level that will maximize profit10-dollars. Find the7. A cylindrical can without a top is to be made to have volume 100 cubic centimeters. Find the8. Find the dimensions of the rectangle of largest area that can be inscribed in a semicircle of400radius of the base and the height of the can which wil minimize the cost of the canradius 6. Wthe origin, of radius r is y = Vr2-hat is the area of the rectangle? (Note: The equation of a semicircle, centered at29. Draco spent $1000 to purchase some stock. He tracked the performance of his investment for20 days. A function that shows the value of his stock V (dollars) at time t days after hispurchase is given by V(t)--3t8260t+1000. At what time did the investment havethe most value?10. Barry runs a chalk manufacturing company. It costs the company $1 to make each box ofchalk. When the company sells the cmillion boxes per year. Find the price that Barry should charge for a box of chalk in order tomaximize his annual profithalk for $p per box, they are able to sell q(p)p +1p311. At what point on the curve y 3-32 +3 does the tangent to the curve have the smallestslope? What is the slope at this point?192

Question
Asked Apr 8, 2019

Solve and explain Q#7

ll T-Mobile
8:25 PM
96%
Section 23 - Exercises (answers follow)
e numbers z and y such that z +y 150 and zy is maximized
su
1. Find non-negative
2. You are to enclose a rectangular garden having an area of 3,600
square meters and surround
it by a fence. How can this be done using the least amount of fencing?
3. What are the dimensions of an open (no top) rec
tangular box that has a square base, a
capacity of 32,000
cm3, and is constructed using the least amount of material?
4. If a manufacturer charges p(x) dollars per item, where p(r) = 4-121 then
thousand ite
will be sold
(a) Find an expression for the total revenue from the sale of x thousand items
(b) Find the value of z that leads to maximum revenue.
(c) Find the maximum revenue.
oduction of widgets the marginal revenue and marginal cost (in thousands of dollars
+ 10
per item) for producing z widgets are given by R()70-z and ()0.122 +4
(a) What is the number x at which these are equal?
(b) Interpret the result: for what value of x is profit maximal?
6. Ifx units are produced, the cost of production is C(z)
400 + 2x+ 0.05x2. In order to
sel units it is known that the price per unit should be p(x)
production level that will maximize profit
10-
dollars. Find the
7. A cylindrical can without a top is to be made to have volume 100 cubic centimeters. Find the
8. Find the dimensions of the rectangle of largest area that can be inscribed in a semicircle of
400
radius of the base and the height of the can which wil minimize the cost of the can
radius 6. W
the origin, of radius r is y = Vr2-
hat is the area of the rectangle? (Note: The equation of a semicircle, centered at
2
9. Draco spent $1000 to purchase some stock. He tracked the performance of his investment for
20 days. A function that shows the value of his stock V (dollars) at time t days after his
purchase is given by V(t)--3t8260t+1000. At what time did the investment have
the most value?
10. Barry runs a chal
k manufacturing company. It costs the company $1 to make each box of
chalk. When the company sells the c
million boxes per year. Find the price that Barry should charge for a box of chalk in order to
maximize his annual profit
halk for $p per box, they are able to sell q(p)
p +1
p3
11. At what point on the curve y 3-32 +3 does the tangent to the curve have the smallest
slope? What is the slope at this point?
192
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ll T-Mobile 8:25 PM 96% Section 23 - Exercises (answers follow) e numbers z and y such that z +y 150 and zy is maximized su 1. Find non-negative 2. You are to enclose a rectangular garden having an area of 3,600 square meters and surround it by a fence. How can this be done using the least amount of fencing? 3. What are the dimensions of an open (no top) rec tangular box that has a square base, a capacity of 32,000 cm3, and is constructed using the least amount of material? 4. If a manufacturer charges p(x) dollars per item, where p(r) = 4-121 then thousand ite will be sold (a) Find an expression for the total revenue from the sale of x thousand items (b) Find the value of z that leads to maximum revenue. (c) Find the maximum revenue. oduction of widgets the marginal revenue and marginal cost (in thousands of dollars + 10 per item) for producing z widgets are given by R()70-z and ()0.122 +4 (a) What is the number x at which these are equal? (b) Interpret the result: for what value of x is profit maximal? 6. Ifx units are produced, the cost of production is C(z) 400 + 2x+ 0.05x2. In order to sel units it is known that the price per unit should be p(x) production level that will maximize profit 10- dollars. Find the 7. A cylindrical can without a top is to be made to have volume 100 cubic centimeters. Find the 8. Find the dimensions of the rectangle of largest area that can be inscribed in a semicircle of 400 radius of the base and the height of the can which wil minimize the cost of the can radius 6. W the origin, of radius r is y = Vr2- hat is the area of the rectangle? (Note: The equation of a semicircle, centered at 2 9. Draco spent $1000 to purchase some stock. He tracked the performance of his investment for 20 days. A function that shows the value of his stock V (dollars) at time t days after his purchase is given by V(t)--3t8260t+1000. At what time did the investment have the most value? 10. Barry runs a chal k manufacturing company. It costs the company $1 to make each box of chalk. When the company sells the c million boxes per year. Find the price that Barry should charge for a box of chalk in order to maximize his annual profit halk for $p per box, they are able to sell q(p) p +1 p3 11. At what point on the curve y 3-32 +3 does the tangent to the curve have the smallest slope? What is the slope at this point? 192

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Expert Answer

Step 1

Suppose r denotes the radius of the base and h denotes the height of the can.

Step 2

Note that the volume of a cylinder with radius r and height h is V = π r2 h.

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Step 3

Since, the top of the can is open, the surface area of the can is S = πr2 + 2&p...

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