Posted by j on Saturday, April 9, 2011 at 7:58pm.
A rectangular box is to be constructed from two different materials. The box will have a square base and open top. The material for the bottom costs $4.25/m2. The material for the sides costs $2.50/m2. Find the dimensions of the box with the largest volume if the budget is $500 for the material

calculus  bobpursley, Saturday, April 9, 2011 at 9:21pm
Volume=a^2 h
cost= 4.25*a^2 + 2.5*(4 a*h)
dV/da=2ah+a^2 dh/da=0
but on the cost equation
take the derivative of Cost respect to a
0=8.5a+10h+ 10a*dh/da
but in the volume equation we can find
dh/da=2ah/a^2=2h/a
put that into the derivative of the cost
0=8.5a+10h+10 a(2h/a)
0=8.5a10h
h=.85a
now you can put that into the cost equation, with cost at 500, and solve for a, then h.
Answer This Question
Related Questions
 Calculus  Suppose that you are to make a rectangular box with a square base ...
 Calculus  A rectangular box is to have a square base and a volume of 20 ft3. If...
 Calculus  1. A rectangular box is to be constructed from 2 different materials...
 Math  A rectangular box is to have a square base and volume of 78 feet cubed. ...
 Calculus  A rectangular box is to have a square base and a volume of 20 ft3. ...
 calculus  A rectangular box is to have a square base and a volume of 50 ft3. ...
 calculus  A rectangular box is to have a square base and a volume of 50 ft3. ...
 calculus  A rectangular box is to have a square base and a volume of 50 ft3. ...
 calculus  A rectangular box is to have a square base and a volume of 50 ft3. ...
 Applied Calculus  A rectangular box is to have a square base and a volume of 50...
More Related Questions