Optimizing Volumes and Surface Areas Using
The U.S Postal Service will accept a
box for domestic shipment only if the sum of the length and girth (distance
around) does not exceed 108 in. Find the dimensions fo the largest acceptable
box with a square end.
2. a) Write an expression that represents the Postal Service's specifications for acceptable boxes in terms of l (length) and g (girth).
108 = _________________
b) Solve the above equation for g. This equation will be used to find the dependent variable, g, in the spreadsheet. g = __________________
Before you type the formula into the spreadsheet in cell, C6, write it down using the cell references. For the greatest acceptable length and girth cell reference you will need to use absolute references, because it will never change, so use $E$2. s = ________________Type this into the spreadsheet and fill down.
c) Next, write an expression that represents the edge of the square end of the box, in terms of g (girth). Before you type the formula into the spreadsheet in cell, D6, write it down using the cell references. s = _______________ Type this into the spreadsheet and fill down.
3. a) Write an equation that represents the volume of the box in terms of l (length) and s (side). volume = __________________ Now you will need to write this formula using cell references. You only need to do it for the first cell in the first row, because you will "fill down" for the rest of the column. volume = ___________________
4. Now that the spreadsheet is filled in you need to determine the dimensions of the largest possible box with a square end and record them here. ________________________
problem: A tank with a rectangular base and rectangular sides is to be open
at the top. It is to be constructed so that its width is 4 meters and its
volume is 36 cubic meters. If building the tank costs $10 per square meter
for the base and $5 per square meter for the sides, what is the cost of
the least expensive tank?
Need more problems on which you can practice? Go on to the next page.