For your nonlinear programming assignment, we will be looking at a production process in which we will be producing a product that has an exponential function in its cost curve: glass bottles. This is a simplification of the process, but essentially certain kinds of glass production must be planned well in advance because the molten glass is destructive to the molds and devices that work with it. So, the more bottles of the glass that we want to produce, the heavier-duty our machinery must be for that production run!

Imagine that we produce bottles and that we sell the bottles in crates of 100. Each crate of bottles sells for $15. The cost function for each crate of bottles reflects the toughness of the machines needed to run them. If we plan to produce a large number of bottles, then our refractory for that run has to be built to withstand it. So, we will assume the cost to be $0.0025 times the number of crates squared.

The only constraint is the amount of bromine we have available, which goes into the glass to provide the brown color. We have 5 bottles of bromine available, and each crate takes of a bottle.

What is the optimal number of crates of bottles to manufacture? Assume that we CAN manufacture partial crates (i.e. this does not have to be an integer problem!)

Remember to use the GRG Nonlinear engine in Solver, and be aware that this Solver engine can run much slower than the Simplex LP engine.

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