Your business transports cars from the factory to dealerships. A car carrier holds 10 cars. You are paid $10,000 for shipping a carrier-load of cars from the factory to the dealership. During loading, transporting, and unloading, the cars' paint may get chipped or the bodies dented. You can minimize potential damage by using better equipment, labor, and procedures. Using top-of-the-line equipment, labor, and procedures guarantees that no cars will get damaged in transit. But top-of-the-line equipment, labor, and procedures cost (amortized) $10,000 per shipment. You can employ cheaper solutions, but cheaper solutions risk damaging cars. On average, each $9 savings due to employing cheaper solutions increases the probablility of any given car being damaged in transit by 0.1 percentage points (that's one-tenth of one percentage point). For example, if you use equipment, labor, and procedures costing $10,000 per shipment, the probability of any given car being damaged in transit is 0%. If you use equipment, labor, and procedures costing $9,991 per shipment, the probability of any given car being damaged in transit is 0.1%. If you use equipment, labor, and procedures costing $9,982 per shipment, the probability of any given car being damaged in transit is 0.2%, etc. If two or fewer cars are damaged, the dealership will repair the cars but will charge you $500 per damaged car. If three or more cars are damaged, the dealership will repair none of the cars and will reject the entire shipment, meaning that you don't get paid for the shipment. Suppose you employ equipment, labor, and procedures costing $8,000 per shipment. Calculate the following: 15. Pr(a given car being damaged) 16. Pr(0 cars damaged in a shipment of 10 cars) (first two digits behind the decimal: 22) (first two digits behind the decimal: 10) (first two digits behind the decimal: 14) (first two digits behind the decimal: 76) 17. Pr(1 car damaged in a shipment of 10 cars) 18. Pr(2 cars damaged in a shipment of 10 cars) 19. Pr(3 or more cars damaged in a shipment of 10 cars) Your only costs are equipment, labor, procedures, and dealer repair reimbursements. Calculate the following: 20. E(revenue per shipment) (first two digits behind the decimal: 78) (first two digits behind the decimal: 33) 21. E(cost per shipment to reimburse dealer for repairs) 22. E(profit per shipment) 23. How much should you spend on equipment, labor, and procedures to maximize your expected profit per shipment? 24. E(profit per shipment)