Hi Guys:

1. A company produces two products whose production levels are represented by

*x*

and

*y. *As a function of these two variables profit is given by:

P(x,y)

= 900*x *‐ 30*x^*2 + 30*xy *‐ 100*y *‐ 10*y^*2 + 2,000

a) What values of *x *and *y *maximize the profit?

b) What is the maximum value of the profit?

c) Verify that the solution is indeed a local maximum.

Just want to make sure I am correct...

a) x = 5 and y = -25

b) -$1,750

c) I am not sure how to go about getting this

2. A local inventor has developed a new camera technology that uses special tubes to

improve the quality of the pictures it takes. To produce, each camera will cost $1,000

of fixed costs, $25 for every tube used, and $400 divided by the number of tubes used

in each camera. The camera sells for $2,025.

a) Write the function

*P(x) *for the profit on a camera, where *x *represents the number

of tubes used in each camera.

b) What obvious restriction must be placed on *x*?

c) Use the function in a) to determine the number of tubes that will maximize profit.

d) Show that *P(x) *is maximized at the stationery point.

Answers (again, tell me if and where I went wrong)

a) R(x) = 2,025x

C(x) = 25x + 400/x

Revenue - Cost = Profit

2,000 x + 400 / x

b) x > 0

I can't figure out C and D to see as I am pretty sure my equation is wrong haha.

Thanks

Ibrox