Answer:
Dimension
Height =29.01
Breadth=38.70
Step-by-step explanation:
Printed area is =386 and margins as specified.
For printed area let height be x and breadth be y.
x*y=386 ⇒ y = 
Now considering the margins
Height = x+6+6=x+12
Weidth =
+8 +8=
+ 16
Area of poster to be minimised =(x+12)(
+ 16)
Differentiate above area with respect to x and equate to zero to find extrema.
= 16 -
=0
x=17.01
Now plug value of x in height and breadth
Height =29.01
Breadth=38.70
Lets see if the gallon fill the paint tray or not.For that purpose we need to find out the volume of the paint tray and compare it with the volume of the gallon.Given:Length = 14 inchesWidth = 10 inchesDepth = 4 cm = 1.57 inches
Volume = length x width x depthVolume = 14 x 10 x 1.57 = 220.47 inches cubeVolume of Gallon = 231 inches cubeComparing the two volumes:231 inches cube - 220.47 inches cube = 10.52 inches cubeHence,The paint will not fill the tray by 10.53 in3.
a) Each of the inequalities determine the semiplane, first semiplane is shaded in red with solid boundary line (because the inequality has sign ≥), second semiplane is shaded in blue with dashed boundary line (because the inequality has the sign <). The common region represents the solution of this system of two inequalities.
b) Pick a point (10,5) from the shaded region. Since

the coordinates of this point are the solution of the system.
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Changes in the dimensions of a geometric solid also causes a change in the volume.
For example consider a cuboid;
Volume = length × width × height
If a dimension of either, the length, the width and the height is increased then the volume will also increase, and vicevarsa.