Friendly Waste Co$.$ runs three different factories and is required by law to safely

dispose of chemicals once a month. Waste from three different factories can be processed

to reduce the amount of two different types of pollutants. State law requires that Friendly

Waste Co$.$s total reduction in the amount of pollutant A is at least $30$ tons and pollutant

B is at least $40$ tons across its three factories. Ultimately, Friendly Waste Co$.$ would like to

minimize the processing cost associated with reducing the two types of pollutants. Because

some factories have better equipment than others, each factory has a different process for

reducing each Pollutant. This information is summarized below. Using the information in the

following table:

Factory Waste $1$ Factory Waste $2$ Factory Waste $3$

Reduction in

pollutant A per ton

of processed waste

$0\mathrm{.}100\mathrm{.}200\mathrm{.}40$

Reduction in

pollutant B per ton

of processed waste

$0\mathrm{.}450\mathrm{.}250\mathrm{.}30$

Processing cost per

ton of waste

$$15$ $$10$ $$20$

Table $1$: Pollutant Reduction and Processing Cost

$$ Formulate the model algebraically. This does not need to be in standard LP form.

$$ Solve the problem using Excel and generate the sensitivity report.

$$ Interpret your answer with respect to the decision variables and the optimal objective

value. How much does it cost to process Factory Waste $1?$ How much does it cost to

process Factory Waste $2?$ How much does it cost to process Waste $3?$

$$ A new local environmental regulation causes the processing cost for each factory waste

to increase by $$2.$ Would the optimal solution change in terms of the amount of waste?

Why?

$$ Using the problem$$s original values, suppose a new government regulation required a

reduction of Pollutant A to be $31\%.$ How would that affect the problem?

$$ Using the problem$$s original values, suppose a new government regulation required a

reduction of Pollutant A to be $34\%.$ How would that affect the problem?