Please submit your solutions via Canvas as two separate files: 1) the formulations for Problem 1 and Problem 2a handwritten and scanned, or electronically-generated whichever you prefer is fine, as long as it is legible) and 2) the Excel file, with optimal solution dearly identified, for Problem 20Each individual student should submit his/her own solutions. You are allowed to work with other students, but you must acknowledge this and identify the students you worked with as part of your submission 1 An airline is purchasing a new tractor for a tractor trailer train to bring age to and from the airplanes. A new mechanised luggage system will be installed in 3 years, so the tractor will not be needed after that. However, it will receive heavy so that the operating and maintenance costs will increase rapidly as the tractor ages. Therefore, it may be more economical to replace the tractor after 1 or 2 years. The following table gives the total corted cost asociated with purchasing a tractor purchase price in trade- owneus operating and maintenance costs at the end of year and trading it in at the end of year bear is now $8.000 $18.000 $10.000 $31.000 $21.000 $12.000 At what times (if any) should the tractor should be replaced to minimize the total cost for the tractors over 3 years? Formulate this problem as a shortest path problem by drawing and clearly labeling the network. What is the optimal replacement policy? 2. Boyle Transportation is a logistics company that specialios in hauling extremely valuable and/or hazardous materials. Unsurprisingly maintaining a clean driving safety record is very important to the company. This helps them to maintain a good reputation and low insurance premiums. The company is also aware that when carrying hazardous materials the environmental consequences of even a minor accident could be disastrous While most logistics companies try to find out that provide the fastest or least costly transportation, Boyle Transportation always tries to select routes that are least likely to result in an accident. The company is currently trying to identify the safest routes for carrying a load of hazardous materials from Los Angeles to Amarillo, Teas. The following network summarizes the routes under consideration. The numbers on each ar represent the probability of having an accident on each potential leg of the joumey 2. Boyle Transportation is a logistics company that specializes in hauling extremely valuable and/or hazardous materials. Unsurprisingly, maintaining a clean driving safety record is very important to the company. This helps them to maintain a good reputation and low insurance premiums. The company is also aware that when carrying hazardous materials, the environmental consequences of even a minor accident could be disastrous. While most logistics companies try to find routes that provide the fastest or least costly transportation, Boyle Transportation always tries to select routes that are least likely to result in an accident. The company is currently trying to identify the safest routes for carrying a load of hazardous materials from Los Angeles to Amarillo, Texas. The following network summarizes the routes under consideration. The numbers on each arc represent the probability of having an accident on each potential leg of the journey. Flagstaff Albuquerque 0.006 Las Vegas 0.001 0.001 Amarillo 0.003 Los Angeles 0.010 0.006 0.002 0.010 0.004 0.006 0.009 0.004 0.002 0.005 0.002 Phoenix 0.003 San Diego Lubbock 0.010 Tucson 0.003 Las Cruces a. Formulate this problem as an integer program. b. Solve using Excel Solver (hint: the objective function will be non-linear...so use a non-linear solver)