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Part $1$

Consider the following LP problem developed at Zafar$$ Malik's Carbondale,$$ Illinois, optical scanning$$ firm:

Maximize

Zequals$=$

$11$Upper X $1$X$1$plus$+11$Upper X $2$X$2$

Subject$$ to:

$22$Upper X $1$X$1$plus$+11$Upper X $2$X$2$less than or equals$100100$

$($C$1)$

$11$Upper X $1$X$1$plus$+22$Upper X $2$X$2$less than or equals$100100$

$($C$2)$

Upper X $1$X$1,$Upper X $2$X$2$greater than or equals$0$

Part $2$

The optimum solution$$ is:

Part $3$

Upper X $1$X$1$

$=$

$33\mathrm{.}3333\mathrm{.}33$

$($round your response to two decimal$$ places$).$

Part $4$

Upper X $2$X$2$

$=$

$33\mathrm{.}3333\mathrm{.}33$

$($round your response to two decimal$$ places$).$

Part $5$

Optimal solution value Z$=$

$66\mathrm{.}6666\mathrm{.}66$

$($round your response to two decimal$$ places$).$

Part $6$

If a technical breakthrough occurred that raised the profit per unit of

Upper X $1$X$1$

to

$ $3$$$3,$

due to this$$ change, the optimal solution

changes

$.$

Part $7$

As a result of the technical$$ breakthrough, the optimum solution$$ is:

Part $8$

Upper X $1$X$1$

$=$

$33\mathrm{.}3333\mathrm{.}33$

$($round your response to two decimal$$ places$).$