So I have been under a lot of stress lately and have been trying to complete things for my other units. Because of this I have neglected maths for the last two weeks (I am catching up this weekend) and I am unable to complete these online quiz questions. I am probably breaking some kind of forum rule by asking you guys for direct answers, but I would really appreciate it (as I have tried for ages and I just have no idea how to do them)

1.

The total profit $P, generated from the production and marketing of n items of a certain product is given by

How many items should be made for maximum profit? What is the maximum profit?

P = −46800 n−6 n ^{3}+1350 n^{2}−116

Enter your answers as a list [in square brackets] of the form: [n,p]

for some number of itemsnand profitp(in dollars, but don't include the dollar sign).

2. Find the value of x that minimises

for positive x.

y = 10 x ^{2}+2700

x

a.

In order to do that first find the derivative dy/dx.

dy/dx =

b.

How many critical numbers does y have, for positive x?

Recall that acritical numberof a function is a value of x for which the derivative of the function is zero or doesn't exist.

c.

What is the nature of the critical number of the previous part?

Enter m forminimum, M formaximumor i for ahorizontal point of inflection.

3.

A piece of cardboard measures 5 cm by 8 cm. Two equal squares are removed from a 5 cm side as shown below. Two equal rectangles are removed from the other corners so that the remaining material can be folded to form a rectangular box with a lid.

(image that goes with it) http://desmond.imageshack.us/Himg826...if&res=landing

4.

You have been asked to design a can shaped like a right circular cylinder with height h and radius r. Given that the can must hold exactly 30 cm^{3}, what values of h and r will minimise the total surface area (including the top and bottom faces)? Give your answers correct to 2 decimal places as a list [in brackets] of the form: [h,r]

for constantsh(height),r(radius), in that order.

I would really appreciate any help given. Thankyou.