Question

Hi, im having trouble figuring these out. please help
1: Find the dimensions of an open

rectangular box of maximum volume and having an area of 192 ft²

 that can be constructed from a piece of cardboard. (Let l represent the length in feet, w the width in feet, and h the height in feet of the box.) 

(l, w, h) =    

What is the volume of the box in ft³

2: Ross-Simons Company has a monthly advertising budget of $53000. Their marketing department estimates that if they spend x dollars on newspaper advertising and y dollars on television advertising, then the monthly sales will be given by the following equation.

z = f(x, y) = 100x^0.1 y^0.9

Determine how much money Ross-Simons should spend on newspaper ads and on television ads each month to maximize its monthly sales. (Give your answers correct to 2 decimal places.)

$  (newspaper ads)

$  (television ads)

3: Postal regulations specify that a parcel sent by parcel post may have a combined length and girth of no more then 108 in. Find the dimensions of the cylindrical package of greatest volume that may be sent through the mail. What is the volume of such a package? (Hint: The length plus the girth is 2πr+l and the volume is πr²l, where l is the length and r is the radius of the package.) (Give your answers correct to 1 decimal place.)r=  inl=  inV=  in³

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