1. A company produces two products whose production levels are represented by
y. As a function of these two variables profit is given by:
= 900x ‐ 30x^2 + 30xy ‐ 100y ‐ 10y^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
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.