Question

Calculus optimisation question

Answer 1

Locate Point B to minimise cost of construction.

Answer 2

What's the part you're confused on? Can you show us what you've come up with as a setup so far?

To find a local minimum or maximum you'll be finding the critical point(s), which involved finding the derivative of a function. You need to make some functions first! ;-D

Answer 3

Thanks for helping.
I am unsure of the functions i need to come up with. Would i use pythagoras?

Answer 4

Can you identify your given stuff first? Constants, rates, etc?

Answer 5

So far i have 4 + (5-x)^2 = r^2 where r is that diagonal

Answer 6

Rate for underwater piping: 240000 \(\large{\frac{$}{mi}}\)
Rate for overland piping: 170000 \(\large{\frac{$}{mi}}\)

Answer 7

If 'x' = miles, then the cost of each pipe option to run x miles is?

Answer 8

Use Pythagoras theorem to find out the point B. Like (5-x) and use it in the equation of hypotenuse. Then use your cost parameters to make the cost equation. Differentiate and equate it to zero to solve.

Answer 9

sorry, i am confused... rate of under water piping is 240000/x ?

Answer 10

(240000 \(\large{\frac{$}{\cancel{mi}}}\))(x \(\cancel{mi}\)) = $240000x

Answer 11

miles cancel out, then what @Champs is saying is spot on

Answer 12

Construct cost equation and differentiate