Suppose you work for a company where one of your responsibilities concerns the secure delivery of specialty computer parts from Scarborough to Kingston, Ontario. The delivery is made with an environmentally friendly truck whose ethanol consumption is described by the function 1 E(x) = 1/250(1200/x + x) In this function, x represents the constant speed (in km/hr) at which the truck is driven and E(x) gives the gas consumption in liters/km. We assume x > 5, the truck driver is paid $20 per hour to drive the 250 km from Scarborough to Kingston, and ethanol costs (an inexpensive) 80 cents per liter. (a) Find the function C(x) that gives the total coin dollars of the driver plus fuel for a truck for the trip from Scarborough to Kingston. (b) Find the marginal cost function when x = 75 and when x = 90. (c) Calculate the speed (rounded to 1 decimal) at which the marginal cost function is equal to zero.
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