Calculus Optimization?

Question

Stellar steel can produce x tonnes of regular-quality steel and y tonnes of super quality steel per day, where y=40-5x 10 - x. The market price for regular quality steel is half the market price for super-quality steel. How many tonnes of regular - quality steel should the company produce to maximize revenue?

Answer 1

y=40-5x 10 - x.
You miss something

Answer 2

a million) it extremely is trouble-free; ==> First choose for the purpose of the situation; right here it extremely is paper dimensions, so as that its section would be minimum; then next comes below what constraints this should be executed? ==> nicely, right here on the chosen paper, you're leaving some margins throughout and arriving on the section for printing, that's given some fastened value. 2) Now, we are clean what we choose for; the thank you to proceed for development mathematical equations, so as that it extremely is solved for determining to purchase the top answer: 3) right here we are given the printing section as 50 squarewherein is consistent; subsequently enable us to start from this expertise; ==> enable the measurement of the printing section be x in (top clever) by utilising y in (width clever) ==> Printing section = xy = 50; == y = 50/x -------(a million) 4) there's a margin of four in each and each at good and backside are offered; subsequently commonplace top of the paper is "x + 8" in; further a margin of two in is offered on the two factors; ==> commonplace width = y + 4 in 5) subsequently the component of the paper is = (x+8)(y+4) 6) Substituting for y from equation (a million), A (x+8)(50/x + 4) = 50 + 4 hundred/x + 4x + 32 7) subsequently the function to be minimized is: A = eighty two + 4x + 4 hundred/x 8) Differentiating this, A' = 0 + 4 - two hundred/x^2 = 4 - 4 hundred/x^2 9) Equating A' = 0, x^2 = one hundred; ==> x = +/- 10 in 10) yet a measurement won't be able to be damaging, subsequently we evaluate only + 10; So x = 10 in and y = 5 in 11) even if we must be sure,in spite of if it extremely is minimum or optimum; for which we can stick to 2d by-product try; So lower back differentiating, A'' = 800/x^3; at x = 10, A'' is > 0; subsequently it extremely is minimum for this reason we end for the printing the section to be 50 squarein, below the given constraints of margins, the outer length of the paper could be 18 in by utilising 9 in; So outer section is = 162 squarein. wish you're defined; have a effective time.

Answer 3

I don't know what your equation is saying.
Here is a good set of things to do for optimization problems.
1. Ask yourself what you know and don't know.
2. Draw a picture.
3. Assign a symbol, like "x", to each unknown quantity and some special symbol, like a capital letter (I'll use Q), to the quantity that is to be optimized.
4. Express Q in terms of the other symbols.
5. Find mathematical statements that relates the other variables to Q and use those equations to eliminate all but one of the variables that is in the expression for Q. Thus, Q is expressed as a function of one variable, say, x.
6. Take the derivative and use the facts about a derivative to find the maximums or minimums.
Hopefully that helps.

Answer 4

rev is rev(x,y) and there's a relationship between x, y

let p be price for reg steel, then 2p is price for super quality

rev = p*(amount of reg steel) + 2p*(amount of sup qual steel)

use x where it belongs and the x-y relationship to get y and put it where it belongs. You then have an equation of rev(x), differentiate, set to zero and solve for max or min.

Answer 5

y=40-5x 10 - x

what does that mean?

Answer 6

you say y=40-5x 10-x
can you clarify this please?

Answer 7

Please be clear about y's expression.