Linear Optimization

A local charity group has a community outreach program that trains residents for two types of recycling and community cleanup activity and is planning a big recycling weekend effort to tidy up the city and generate funds to support further outreach. With limited volunteers, they need to determine how to best prioritize their recycling efforts.

Recycling plastic bottles generates proceeds of $\backslash (\backslash$$ $16\backslash )$ per bag and a volunteer can gather $5$ bags per hour. Recycling aluminum cans generates proceeds of $\backslash (\backslash$$ $28\backslash )$ per bag and a volunteer can gather $3$ bags per hour.

The charity expects to have $100$ volunteers.

To ensure that both kinds of recycling are collected, the city wants at least $\backslash (25\backslash \%\backslash )$ of the volunteers collecting cans and at least $\backslash (30\backslash \%\backslash )$ collecting bottles.

Write a Matlab script that uses linprog to determine the number of volunteers to use collecting each type of recyclable to maximize fund generation. Let a variable named vols be your solution vector, representing the numbers of bottle$-$collecting and can$-$collecting volunteers, in that order.

Have your script clearly say how many volunteers should be trained to collect each type of recycling. Have it print the hourly fundraising for the recycling effort when volunteers are organized the way you have determined.

$($Hint: When testing in normal Matlab, the result might change if the proceeds for plastic were $\backslash (\backslash$$ $17\backslash )$ per bag.$)$

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$\%$ Our vols variable will be $[$number of plastic bottle volunteers, number of aluminum can volunteers$]$

$\%$ It would be smart to define things like the amount of each recyclable that can be collected per hour

$\%$ the value of each bag of the recyclables.

$\%$ Our objective function is the total value of collected recycling per hour,

$\%$ We will have to swap the sign.

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