Question

Calculus Optimization?

Answer 1

For the cost function C(x) = 720 + 4x + 0.02x^2 dollars and price function p(x) = 15 - 0.002x dollars, find the production level that will maximize profits. (An explanation of what to do would be amazing cause I am so stuck)

Answer 2

similar to manhini

Answer 3

except first we need to combine the function so that we can get profit
so p(x)-c(x) is equal to profit(x)

Answer 4

then you take the first derivative of your PROFIT function and set that equal to 0 and find the critical points
then you take the second derivative and DO NOT set equal to zero but take your numbers from the first derivative and plug them in.
if from the second derivative your plugged in values get an answer less than

Answer 5

well how would i plug in points into the second derivative since there is no x?

Answer 6

i meants values

Answer 7

there is from your first derivative

Answer 8

also someone made a good point in manhani's question. sometimes you won't need the second derivative test.

Answer 9

find the critical points! its all values plugged into the first derivative that get 0, these x values will tell you where your mins and maxs are

Answer 10

ok well for p(x) i got -.02x^2 -4.002x - 705 and then for the derivative i got 0.4x + 4.002 but that gives me a negative number

Answer 11

you are right... there is something i must be not understanding

Answer 12

your cost and price functions are correct?

Answer 13

could you type the question exactly as it is given

Answer 14

that value is -100.05 but isnt that the minimum? I want the max

Answer 15

how i posted the question up there is how it was given

Answer 16

? but thats impossible, your cost is extremely big... what you are saying is that this company is paying a lot more than they are selling the product for

Answer 17

negative profit

Answer 18

you are sure the equations are correct

Answer 19

exactly thats why im confused. I am assuming that it indicates that if the company does not sell anything the cost of running it will make its profit be negative

Answer 20

the original equations in my problem yes, but the ones im using based on p(x) - c(x) no im not sure

Answer 21

no your p - c is correct i did it myself but again it doesn't make sense

Answer 22

your company in the problem has significant money issues

Answer 23

unless im reading this completely wrong

Answer 24

the back of the book says the answer is 250 but i have no idea where they got that from

Answer 25

hey look at your P(X) you put down 15 - 0.002x

Answer 26

are you SURE there isn't also some kind of x^2 somewhere there?

Answer 27

yes that is correct

Answer 28

no if i could show u a picture of the book i would

Answer 29

it says 15 - .002x

Answer 30

then try asking someone else see if they get something else im sorry

Answer 31

I think I'll just go into tutorials and ask for help because if your lost and im lost then yeah

Answer 32

thanks for the help though

Answer 33

hey can you message me about this if you get the answer? im really curious

Answer 34

hahaha sure how do i do that? is their like a friend list option or something or do i have to search for ur profile?