Buffets Army $$ The Willy Buffett Foundation $($WBF$)$ each summer hires local high school

and college students with local ties to staff its many camp and outreach activities around the

upper Midwest. For the upcoming summer, based on cost and demand for student worker help,

it can target to hire up to $600$ high school $($HS$)$ students and college students $($CO$)$ combined.

The Foundation will NOT target to hire more than $600,$ but could target to hire less depending

upon other factors $($described below$).$

Because the Foundation has been doing this for a number of summers, they have developed a

metric that measures the $$attractiveness$$ of the HS and CO hires. This metric combines

productivity and cost. Higher levels of this measure $($call it a Buffetmeter$)$ is better than lower

levels. For this summer, assume that the Buffetmeter for a HS student is $300,$ while the

Buffetmeter for a CO student is $700.$

Due to local arrangements with the area high schools, the WBF has agreed that no more than

$40\%$ of the total students hired this summer can be college students $($CO$$s$).$ Additionally,

history has also shown that some students who agree to come invariably never show up$.$ This

$$drop$-$out$$ rate tends to be $5\%$ for the HS students and $10\%$ for the CO students. WBF wishes to

target students such that the total expected number of $$drop$-$outs$$ is no greater than $35.$

The WBF wishes to find the optimal number of high school students $($HS$)$ and college students

$($CO$)$ to target to hire such that the overall Buffetmeter measure is maximized, and that the hiring

constraints of the situation described above are met.

Note that you are deciding on how many students of the two types to TARGET to hire. Drop out

information constrains the decisions of the models, but don$$t make the problem more complex

than it is$.$

Part II: Mechanics. Given the following LP models $($represented abstractly with decision

variables X and Y$),$ find the optimal solution using the $$graphing$$ approach.

Your solution MUST show the following:

A$)$ Graph

a$.$ Plotting all $3$ constraints

b$.$ Shading in the feasible region of the entire LP model

c$.$ Identification of the relevant extreme points

B$)$ Relevant Extreme Points

d$.$ Calculate the $($X$,$Y$)$ values of each relevant Extreme Point

e$.$ Show the algebraic calculations of how the $($X$,$Y$)$ values of the Extreme Points

were calculated $($eyeballing a picture is not sufficient$).$

C$)$ Optimal Solution

f$.$ Evaluate each Extreme Point by the objective function

g$.$ Identify which extreme point is the $$best$.$