Let x ----------> the height of the whole poster <span>y ----------> the </span>width<span> of the whole poster </span> We need
to minimize the area A=x*y
we know that (x-4)*(y-2)=722 (y-2)=722/(x-4) (y)=[722/(x-4)]+2
so A(x)=x*y--------->A(x)=x*{[722/(x-4)]+2} Need to minimize this function over x > 4
find the derivative------> A1 (x) A1(x)=2*[8x²-8x-1428]/[(x-4)²]
for A1(x)=0 8x²-8x-1428=0 using a graph tool gives x=13.87 in
(y)=[722/(x-4)]+2
y=[2x+714]/[x-4]-----> y=[2*13.87+714]/[13.87-4]-----> y=75.15 in
the answer is <span>the dimensions of the poster will be </span>the height of the whole poster is 13.87 in the width of the whole poster is 75.15 in
If two gallons of paint covers 3 rooms then you need to divide 15 gallons of paint by 2 gallons of paint = 7.5 gallons of paint. then you need to multiply 7.5 gallons of paint by 3 rooms = 22.5..... so that means you can paint 22 full rooms.
