$($please answer it on a paper$)$

$1-$ The IT department is considering buying several computers of three

types, Supreme, hux, and super. The table below shows the

characteristics of each.

For service purposes, the number of Lux computers should at least be $50\%$ of

the total number of computers. The annual maintenance cost should not

exceed $$3000.$ The total area available for computers is $40m^2.$ The computers

have to serve at least $500$ people The total available budget is $$100,000.$

Formulate the above as a linear program problem so as to maximize the

number of computers

$2--$Consider the following LP problem

min$10x1+x2$

st$.$

$2x1+326$

$x1c=2$

$31-420$

Plot the problem

Ideatify the feasible solution space

Identify the candidate optimum points

a$)$ Find the optimal values of the variables and objective function

b$)$ Identify the binding constraints

c$)$ Calculate the slack$/$surplus of each

d$)$ Identify the non$-$binding constraints

e$)$ Calculate the slacks$/$surplus of each

f$)$ Identify the redundant constraints

g$)$ What is the maximum allowed increase of resource $1$

h$)$ Calculate the unit worth of resource $2$

i$)$ Calculate the unit worth of resource $3$

j$)$ Comment on the values of the unit worth obtained in parts $($k$)$ and $($l$)$

$3-$ In formulating problem $1$ and problem $2,$ mention the main assumptions made

and briefly explain each,