Problem $3-$ Optimization and Sensitivity Analysis $-$ Buckeye Systems $(30\%)$

Using the information provided, create a linear program using solver in the 'Problem $3-$ Part $1\text{'}$ sheet in the provided Excel workbook. Then create a sensitivity analysis using that optimization model to answer the questions on the problem $3-$ part $3$ answers sheet

Part $1-$ Construct an optimization model using the information and the table provided on the next page

Buckeye Systems is a systems integrator located in Columbus, Ohio. Each year they make wholesale purchasing arrangements with manufacturers to acquire electronic components that they then assemble into computers for retail sale or custom orders. The order deadline for this year is rapidly approaching and they just received an unexpected order from THE Ohio State University for new lab computers. Even worse is that their entire acquisistions team went to Miami for Spring Break and have decided that they will not be returning to Ohio, leaving no one at Buckeye Systems able to identify how much of each component should be ordered.

You and your team have been brought in as consultants to identify how much of each component should be ordered before the deadline passes. The CEO has briefed your team on whats available to be purchased and the constraints facing Buckeye Systems, he also informs you that he is trying to maximize annual profit so that he can buy a new yacht.

While the CEO briefed you on the constraints, your team took the following notes:

The warehouse currently has $75$ assembley workers, who each work $40$ hours per week, $46$ weeks a year

Some of the computers built have software deals, in which the computer is sold with extra software installed, each computer sold with this additional software bundled in brings Buckeye Systems an extra $$150$ on top of the computers sale price.

At least $5,000$ Desktops must be assembled, $10,000$ Laptops, and $10,000$ Minis

There is a custom order from THE Ohio State University for exactly $10,000$ new Lab PCs

To spread risk and not oversaturate the market, some limits are set on high$-$end and ultra$-$high$-$end computers

At least $40\%$ of total profit must come from computers not specified as high and ultra$-$high

No more than $10\%$ of total desktops and laptops sold can be specified as high and ultra$-$high

Lastly, at least $50\%$ more low$-$end Mini computers need to be made than low$-$mid$-$end Mini computers

The table provided shows various statistics about each computer Buckeye Systems builds, with each $\text{'}x\text{'}$ indicating that the given component is used in the assembely of that particular computer model.

NOTE: Normally a problem like this would include an integer constraint as its not possible to build a partial computer using partial components. However, you can not generate a solver sensitivty report with an integer constraint, so do not include one in your problem!