Death and Piecewise Linear Functions

Although this may seem a little gruesome, it is not uncommon for businesses to give discounts for volume sales. In this case, a mortician charges less per pound for bodies weighing more than a certain amount.

The local mortician charges by the pound for embalming according to the following table:

piecewise_lin_death_01

Find a piecewise linear function that models the cost as a function of weight.

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How Do You Use Google Sheets To Do Row Operations For The Simplex Method?

In an earlier post, I showed how to set up a standard minimization problem from an application. In another post, I demonstrated how to find the corresponding dual maximization problem and to solve it with the Simplex Method. This algorithm is tedious and prone to arithmetic errors.

In the video below, the steps in the Simplex Methods are carried out in Google Sheets. The same steps can also be carried out in other spreadsheets such as Microsoft Excel.

Please note that there is a typo in the original matrix in the process. The cell in D2 should be a 1 instead of a zero to account for the slack variable in the first constraint.

Rates and Rational Models

pe_quotient_ruleMany situations require us to take the derivative of a quotient. One situation like this is a model of a stocks price to earning ratio. In this situation the price is modeled by a function P(t) and the earnings by E(t).To find the rate at which the PE ratio is changing, you need to need to take the derivative of the model for the PE ratio.

The ratio is modeled by a quotient, P(t)/E(t). Since this is a quotient, we need to apply the quotient rule for derivative, pe_quo_01

but apply this to our functions. This means u will be replaced with P and v will be replaced with E to give

pe_quo_02

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