A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function C(x) = 0.9x^2 -234x + 23,194 . How many cars must be made to minimize the unit cost?Do not round your answer.

Answer:130 cars.Step-by-step explanation:The cost function is given by:C(x) = 0.9x^2 -234x + 23,194; where x is the input and C is the total cost of production. To find the minimum the unit cost, there must be a certain number of cars which have to be produced. To find that, take the first derivative of C(x) with respect to x:C'(x) = 2(0.9x) - 234 = 1.8x - 234.To minimize the cost, put C'(x) = 0. Therefore:1.8x - 234 = 0.Solving for x gives:1.8x = 234.x = 234/1.8.x = 130 units of cars. To check whether the number of cars are minimum, the second derivative of C(x) with respect to x:C''(x) = 1.8. Since 1.8 > 0, this shows that x = 130 is the minimum value.Therefore, the cars to be made to minimize the unit cost = 130 cars!!!