$1.$ A contractor is preparing a bid for the construction of a small office building and plans to use a $2\mathrm{.}4-$cubic$-$yard crawler$-$mounted hydraulically operated backhoe to excavate for the building foundation. He plans to remove the excavated material from the job site with $15-$cubic$-$yard end$-$dump trucks that he owns. TABLE $23\mathrm{.}5$ Weight Distribution for Problem $1$

a$.$ The backhoe cost $$390,000$ to purchase and has an expected useful life of $12,000$ operating hours. Fuel, oil, and minor maintenance are estimated to cost about $$58$ for each hour the back$-$ hoe is used. Major maintenance and repair costs are estimated to be about $55\%$ of the annual straight$-$line depreciation value. The contractor estimates that he will use the backhoe about $1,000$ hours per year and realize a salvage value after $12,000$ hours of about $25\%$ of the acquisition cost. The backhoe operator earns $$60$ per hour. Insurance, interest, and taxes cost about $16\%.$ What is the estimated cost per hour for the contractor to use the backhoe on the project?

b$.$ The dump trucks each cost $$195,000$ to purchase. Fuel, oil, and minor maintenance are esti$-$ mated to cost about $$45$ for each hour a truck is used. Tires cost $$3,500$ to replace $($estimated to occur at every $3,600$ hours of use$).$ Major maintenance and repair are estimated to be about $45\%$ of the annual straight$-$line depreciation value. The contractor estimates the trucks will be used about $1,200$ hours per year. He plans to replace the trucks after $12,000$ hours of use and anticipates a salvage value of about $12\%$ of the purchase price. Truck drivers earn $$55$ per hour. What is the estimated cost per hour for the contractor to use one dump truck on the project?

c$.$ The contractor estimates that the average cycle time for the backhoe will be $45$ seconds, and that its operational efficiency will be $50$ minutes per hour. He determined from the project drawings that the size of the foundation will be $70$ feet by $30$ feet and $12$ feet deep. The material to be excavated is sandy clay with a swell estimated to be $20\%$ and a unit weight of $2,600$ pounds per bank cubic yard. The disposal site for the excavated material is $2$ miles from the project site. The haul road has an average uphill grade of $3\%$ when traveling from the excavation site to the disposal site. The rolling resistance of the haul road is estimated to be $65$ pounds per ton, and the coefficient of traction is estimated to be $0\mathrm{.}5.$ Operational efficiency of the trucks is estimated to be $50$ minutes per hour, and job conditions are considered aver$-$ age. The gear train efficiency of the $250-$horsepower dump trucks is estimated to be $0\mathrm{.}75.$ The maximum load that can be carried safely in the trucks is $17\mathrm{.}5$ tons, and an empty truck weighs $35,000$ pounds. The weight distribution for the trucks is shown in Table $23\mathrm{.}5.$ The maximum rated speed for the trucks is $35$ miles per hour. How many trucks should the contractor use for this hauling operation to minimize his cost?

d$.$ The contractor estimates that he will need a truck tractor and trailer for $1\mathrm{.}5$ hours to haul the backhoe to the project site and another $1\mathrm{.}5$ hours to return the backhoe to his equipment storage yard. How much should the contractor estimate his total cost to be for this excavation and hauling operation? The hourly ownership and operating costs $($including operator$$s wages$)$ for the truck tractor and trailer are estimated to be $$115$ per hour.