A medical equipment industry manufactures xray machines The

A medical equipment industry manufactures x-ray machines. The unit cost C ( The cost in dollars to make each x-ray machine ) depends on the number of machines made. If X machines are made, then the unit cost is given by the function C ( x) = 0.3x^2-186x+43,733. How many machines must be made to minimize the unit cost?

Number of X-Ray machines: __

Solution

unit cost  C(x) = 0.3x²-186x+43733

unit cost  C(x) = (0.3(x²-(186_/0.3)x))+43733

unit cost  C(x) = (0.3(x²-620x))+43733

unit cost  C(x) = (0.3(x²-620x+(620_/2)²-(620_/2)²))+43733

unit cost  C(x) = (0.3(x²-620x+310²-310²))+43733

unit cost  C(x) = (0.3(x²-620x+310²))-(0.3*310²)+43733

unit cost  C(x) = (0.3(x-310)²)-28830+43733

unit cost  C(x) = 0.3(x-310)² +14903 is a parabola opening upwards

vertex is (310,14903)

310 machines must be made to minimize the unit cost

Number of X-Ray machines: 310