A Machine cost $$65,000$ to purchase. Fuel and minor maintenance are estimated to cost $$14\mathrm{.}35$ per operating hours $($those hours when the engine is operating, and the machine is doing work$).$ A set of tires cost $$4,400$ to replace, and their estimated life is $3,200$ use hours. A $$7,500$ major repair will probably be required after $3,500$ hours of use. The machine is expected to last for $9,600$ hours, after which it will be sold at a salvage value equal to $15\%$ of the original purchase price. A final set of new tires will not be purchased before the sale. How much should the owner of the machine charge per hour of use, if it is expected that the machine will operate $1,600hr.$ per year? The company's cost of capital rate is $6\mathrm{.}5\%.$

$[40$ Points$]$