A manufacturer of storage bins, with a budget of $10,000,plans to produce some open -top rectangular boxes with squarebases.The volume of each box is to be 125 cubic feet.Material forthe base costs $ 4 per square foot, and material for the sidescosts $2 per square foot.
Determine the dimensions of the box that will minimise thecosts of materials.Based on material costs alone,how many bins canthe manufacturer produce?
Suppose that the costs are expected to go up to $6 per squarefoot (base) and $4 per square foot (sides), by the end of theyear.How many bins can the manufacturer now produce if she stillwishes to minimze material costs?