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Marina Mines produces iron core at four different mines, however, the ores extracted

at each mines are different in their iron content. Mine $1$ produces manganite ore,

which has $70\%$ iron content; Mine $2$ limonite ore, which has $60\%$ iron content, Mine

$3$ pyrite ore, which has $50\%$ iron content, Mine $4$ taconite ore, which has $30\%$ iron

content. Marina has three customers that produces steel$-$ Armco, Best and Corcon.

Armco needs $400$ tons of pure iron $(100\%),$ Best requires $250$ tons of pure iron and

Corcon requires $290$ tons. It costs $$37$ to extract and process $1$ ton of magnetite ore at

mine $1,$ $$46$ to extract and process $1$ ton of limonite ore at mine $2,$ $$50$ to extract and

process $1$ ton of pyrite ore at mine $3$ and $$42$ to extract and process $1$ ton of taconite

ore at mine $4.$ Marina can extracts $350$ tons of ore mine $1$; $530$ tons at mine $2$; $610$

tons of mine $3$ and $490$ tons at mine $4.$ The company wants to minimize cost and to

meet its customer$$s demand of pure iron. Formulate the LPP model, generate the

sensitivity report and answer the following questions:

a$.$ Write down briefly the sensitivity report, with its feasibility and optimality

ranges.

b$.$ Which mines are bind to the production. Do any mines have slack capacity? If yes

which one$($s$)?$

c$.$ If Marina Mines could increase production capacity at any one of the mines,

which should it be$?$ Why? What will be the implication on the optimal solution?

d$.$ If Marina mines would like to increase the capacity simultaneously, M$1$ increase

by $20,$ M$2$ increase by $50$ and M$3$ increase by $90$ and M$4$ increase by $110$ tons, is

it feasible to do it$,$ what is the implications. Explain and find the optimal cost.

e$.$ If Marina were to determine that it could increase the production capacity at mine

$1$ from $350$ to $500$ tons, at an increase in production costs to $$43$ per ton, should it

do so$?$

f$.$ If any of the customer$$s demand of pure iron will increase, how it will be treated,

and what will be its implication.

g$.$ What is the implication of reduced cost in LPP model.

Thank you!