optimization Q: Suppose that a window must contain 50 square feet of glass...

[optimizationh8tr]

So i have a load of optimization questions to do and am having trouble with most of them can someone teach me how to do this question as it is the basis for the rest of them.
Suppose that a window must contain 50 square feet of glass, and that the outer framing costs $3 per foot while the seam between the semicircle and rectangle costs only $2 per foot find the cost of the cheapest window.
so can anyone help for this one question thanks in advance

 

[Deleted member 4993]

So i have a load of optimization questions to do and am having trouble with most of them can someone teach me how to do this question as it is the basis for the rest of them.
Suppose that a window must contain 50 square feet of glass, and that the outer framing costs $3 per foot while the seam between the semicircle and rectangle costs only $2 per foot find the cost of the cheapest window.
so can anyone help for this one question thanks in advance

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting!!

 

[Harry_the_cat]

So i have a load of optimization questions to do and am having trouble with most of them can someone teach me how to do this question as it is the basis for the rest of them.
Suppose that a window must contain 50 square feet of glass, and that the outer framing costs $3 per foot while the seam between the semicircle and rectangle costs only $2 per foot find the cost of the cheapest window.
so can anyone help for this one question thanks in advance

In any optimization problem like this, the first thing you need to do is to express the variable you are trying to maximise/minimise in terms of another variable.
In this question you need to minimise COST (call it C), so you need to write a formula for cost in terms of another variable (probably base length of window - call it x).
I think you may have more info about the window that you haven't told us. Is it a square window with a semicircle on top? Or a rectangular window with a semicircle on top (if so do you know anything about the relationship between base length and height?) This info is needed to continue.

 

[stapel]

So i have a load of optimization questions to do and am having trouble with most of them can someone teach me how to do this question as it is the basis for the rest of them.

The book and your instructor have provided loads of worked examples, in addition to whatever you've found in your web search. So doing one more example isn't going to make much of a difference. Instead, we'll need to see what you've tried, so we can attempt to figure out what is causing things to go sideways.

Suppose that a window must contain 50 square feet of glass, and that the outer framing costs $3 per foot while the seam between the semicircle and rectangle costs only $2 per foot find the cost of the cheapest window.

Windows are typically rectangular only. From what you've posted, I'll guess that there was a picture that went along with this exercise, which would have explained to us what is meant by "the semicircle". Lacking that information, I will guess that you're working with what is usually called a "Norman" window, where there is a semicircle of glass above the regular rectangle:

. . . . .

You would have started your efforts with what you learned back in algebra: drawing a picture, labelling dimensions, and recalling useful formulas. For instance, how would one relate the width of the window to the diameter (and thus the radius) of the semicircle? And so forth.

Please reply with all of your efforts so far. Thank you!

 

[optimizationh8tr]

ok

i dont really know how to start this question could you help me to start at least

 

[optimizationh8tr]

so yes the window has a shape of a semi circle on top of a rectangle
so far i have made the equation 50=2y+x i dont think this equation is right and am truly stuck

 

[stapel]

so yes the window has a shape of a semi circle on top of a rectangle
so far i have made the equation 50=2y+x i dont think this equation is right and am truly stuck

Let's do the algebra first: For what do "x" and "y" stand? By what reasoning did you obtain this equation? Where are you accounting for the semicircular portion? Where are you accounting for the cost? What geometrical formulas have you applied?

Please be complete. Thank you!

 

[Harry_the_cat]

so yes the window has a shape of a semi circle on top of a rectangle
so far i have made the equation 50=2y+x i dont think this equation is right and am truly stuck

All of these optimisation questions follow the same procedure. I'll walk you through this one, then you can apply the same procedure to the other optimisation questions you have.

Step 1:
Define your variables. (Draw and label a diagram if appropriate.)
I assume that you have let x=base of rectangle (in feet) and y = height of rectangle (in feet). You need to state that first.

Step 2:
Determine what variable it is you are trying to minimise/maximise.
Here you want to minimise Cost (let it be $C).

Step 3:
Get a formula for this variable in terms of your variables defined in step 1.
Write C in terms of x and y.
Hint: Consider the total length of the outer framing, ie the perimeter of your shape. How would you calculate the perimeter if you know x and y? What would the cost of this part be if framing was $3 per foot?
Now calculate the cost of the "inner framing" (the seam) at $2 per foot.
So what is total Cost (C)?

Do this first then I'll show you Step 4.