The American Safety Council must allocate its national budget for the next fiscal year. Irrevocable decisions have already been made concerning various "program areas" and their total funding; for example, a total of $110,000 has been allocated to the prevention of automobile fatalities and reduction of property damage. However, detailed allocation decisions must be made concerning specific projects designed to contribute to the program missions. In the case of automobile fatality prevention and reduction of property damage, the table below contains the projects recommended by council analysts, together with appropriate data. The decision-makers of the council want you to help them make their budget allocation (or project choice and magnitude) decisions. In response to a question concerning which of their two specific missions is more important, they said: "That's a tough question! On the other hand, human life is sacred and cannot be purchased for any amount of money. On the other hand, if there are two competing ways to save the same number of lives, we would naturally prefer the project that also results in the lower amount of property damage." Project 1. Seat belt advertising 2. Research on improved highway design Upper Limit of Expenditure on Project (measured in $) $ 80,000 Expected Fatalities Expected Reduction in Property Damage per $1,000 Expended $ Prevented per $1,000 Expended 0.33 0 20,000 0.25 20,000 75,000 0.15 30,000 automobile design 4. Dollars spent lobbying for tougher state "drunk 100,000 0.27 10,000 driving" penalties 3. Research on improved When asked specifically what "trade-off" between lives saved and property damage would make them be indifferent, they said: "That's really a tough question! However, we are aware that a certain government agency has, for internal resource allocation purposes, an implicit dollar value for human life saved of $300,000 (we think another agency also uses this number in making decisions about building additional safety into their equipment)." Formulate an LP model whose solution would represent an optimal allocation of the budgeted $110,000 based on all the information above. Be sure to define all variables used. You need not solve the formulation.