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Calculus
A piece of wire 6 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (Give your answers correct to two decimal places.)
(a) How much wire should be used for the square in order to maximize the total area?
(a) How much wire should be used for the square in order to maximize the total area?
Calculus
Suppose p is a polynomial with n distict roots. show that p' has n-1 roots.
We have studied MVT and rolles theorem so i would think i need to use them to prove it?
We have studied MVT and rolles theorem so i would think i need to use them to prove it?
Calculus
A company manufacturers and sells x electric drills per month. The monthly cost and price-demand equations are
C(x)=69000+40x,
p=190−x30, 0≤x≤5000.
(A) Find the production level that results in the maximum revenue.
Production Level =
(B) Find the price that the company should charge for each drill in order to maximize profit.
Price =
(C) Suppose that a 5 dollar per drill tax is imposed. Determine the number of drills that should be produced and sold in order to maximize profit under these new circumstances.
Number of drills =
C(x)=69000+40x,
p=190−x30, 0≤x≤5000.
(A) Find the production level that results in the maximum revenue.
Production Level =
(B) Find the price that the company should charge for each drill in order to maximize profit.
Price =
(C) Suppose that a 5 dollar per drill tax is imposed. Determine the number of drills that should be produced and sold in order to maximize profit under these new circumstances.
Number of drills =
Calculus
The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 464 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 8 dollar increase in rent. Similarly, one additional unit will be occupied for each 8 dollar decrease in rent. What rent should the manager charge to maximize revenue?
Calculus
A manufacture has been selling 1400 television sets a week at 420 each. A market survey indicates that for each 21 rebate offered to a buyer, the number of sets sold will increase by 210 per week.
a) Find the demand function p(x), where x is the number of the television sets sold per week.
p(x)=
b) How large rebate should the company offer to a buyer, in order to maximize its revenue?
c) If the weekly cost function is 98000+140x, how should it set the size of the rebate to maximize its profit?
a) Find the demand function p(x), where x is the number of the television sets sold per week.
p(x)=
b) How large rebate should the company offer to a buyer, in order to maximize its revenue?
c) If the weekly cost function is 98000+140x, how should it set the size of the rebate to maximize its profit?
Calculus
A boat on the the ocean is 6 km from the nearest point on a straight shoreline; that point is 10 km from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. If she walks at 5 km/h and rows at 4 km/h. How far will the point on shore be from the restaurant if she plans to minimize her total travel time?
Distance from restaurant =
Distance from restaurant =
Calculus
Consider the function f(x)=2x+5.
If D is the distance from any point on f(x) to the origin:
D=
At what x value is f(x) closest to the origin?
x=
If D is the distance from any point on f(x) to the origin:
D=
At what x value is f(x) closest to the origin?
x=
Calculus
Suppose that a when a cell phone store charges 16$ for a car charger, it sells 45 units. When it drops the price to 15$ it sells 48 units. Assume that demand is a linear function of price. If each phone charger costs 1$ to make, what price should the store charge to maximize its profit?
If x is the number of times the price is reduced by one dollar. Find a function for total profit with respect to x. A negative value for x will mean the price is increased.
f(x)=
Price to maximize profit =
If x is the number of times the price is reduced by one dollar. Find a function for total profit with respect to x. A negative value for x will mean the price is increased.
f(x)=
Price to maximize profit =
Calculus
A carpenter has been asked to build an open box with a square base, where an open box means a box without a top. The sides of the box will cost $6 per square meter, and the base will cost $3 per square meter. What are the dimensions of the box of maximal volume that can be constructed for $144 ?
If x is the length of one of the sides of the base and z is the height of the box. Find a function f(x) for the volume of the box.
NOTE: The function should just be in terms of x.
f(x)=
Let x∗ and z∗ be the dimensions that maximize the volume of the box.
x=
z=
If x is the length of one of the sides of the base and z is the height of the box. Find a function f(x) for the volume of the box.
NOTE: The function should just be in terms of x.
f(x)=
Let x∗ and z∗ be the dimensions that maximize the volume of the box.
x=
z=
Calculus
A piece of wire 50 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.
(a) How much of the wire should go to the square to maximize the total area enclosed by both figures? m
(b) How much of the wire should go to the square to minimize the total area enclosed by both figures? m
(a) How much of the wire should go to the square to maximize the total area enclosed by both figures? m
(b) How much of the wire should go to the square to minimize the total area enclosed by both figures? m
