using matlab code

function F = optfun(pair) x=pair(1); y=pair(2); F = [3*y + .001*y*exp(x)-4*x, x^2 + y^2 - 25]; end

Find the volume of an actual dumpster online or from another source. Any shape would be acceptable, but for simplicity of calculations, a shape like the dumpster in the image below is recommended. While maintaining the general shape, use Lagrange multipliers to determine the dimensions a container of the same volume should have in order to minimize the cost of construction.

Parameters needed for formulating the problem:

• For the purpose of the project, you may simplify the design in any way you choose. For example, you may assume that the sides of the dumpster are completely smooth with no additional hardware.
• The sides, back, and front are to be made from 12-gauge (0.1046 inch thick) steel sheets. Assume this type of metal costs $3 per square foot.
• The base is to be made from a 10-gauge (0.1345 inch thick) steel sheet. Assume this metal costs $5 per square foot.
• Lids cost approximately $50.00 each, regardless of dimensions.
• Research to determine any welding costs (in dollars per foot) to connect the sides and the bottom of the dumpster. Provide whatever sources you use as a hyperlink.