Mark Haynes is interested in buying a new car. He decided on a Particular model, which has lots of options from which to choose. The base price of the car is $16,510 and he allotted a budget of $19,250 to purchase it. The table below shows the possible options over and above the base model that he could choose, their cost, and the utility that he assigned to each option:

All of these are options to replace the base model configuration. Thus, for example, he may choose one of the three engine options or keep the base model engine, choose one of these three warranty options or keep the base model warranty, choose automatic transmission or keep the base model manual transmission, and so on. In addition, if the automatic transmission is chosen, then a three- or five-year warranty must be chosen, and if the fastest engine is chosen, then either the 16-inch or alloy wheels must be chosen.
a. Develop and solve an integer optimization model to maximize his utility and stay within budget.
b. If he has an additional $500 to spend, how would his choices change?
c. In a magazine, Mark found a car stereo system for $300. If he decides to replace the base model radio with this one, how would the model and his decisions change?

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Option Slower engine Faster engine Faster engine No warranty 3-year warranty -year warranty Automatic transmission 15-inch wheels 16-inch wheels Alloy wheels AMFMradio AMFMCD AMFM CD DVD AMBMCD DVD 6 speaker Sunroof Moon roo:f 2-wheel disc brakes 4-wheel disc brakes with ABS Utility -0.10 0.40 0.50 0.00 0.30 0.70 0.80 -0.15 0.25 0.35 0.10 0.30 0.50 0.65 0.25 0.40 -0.10 0.35 Cost S(300.00) S600.00 $1,000.00 S(250.00) $450.00 $750.00 800.00 S(150.00) S300.00 S500.00 S200.00 S300.00 S400.00 S750.00 S50.00 $150.00 S(250.00) $250.00