+18 The cost in millions of dollars for a company to manufacture 𝑥 thousand automobiles is given by the function 𝐶(𝑥) = 5𝑥 2 − 40𝑥 + 98. a. How many automobiles must the company produce to minimize the cost? b. How many automobiles is the company currently producing if the cost is $75.8 million? c. What is the company’s cost if it produces 8000 automobiles?
+128475 a. We have the form ax^2 + bx + c
The number of autos that minimize the cost is -b /2a = - (-40) / (2 (5) ) = 40 / 10 = 4 (thousand)
b. 75.8 = 5x^2 - 40x + 98 subtract 75.8 from both sides
5x^2 - 40x + 22.2 = 0
Quadratic function
x = [ 40 ± sqrt ( 40^2 - 4 (5) (22.2) ) ]/ (2 * 5) = .6 or 7.4 = 600 or 7400 autos....note both ptoduction levels give the same cost
c. 5(8)^2 - 40 (8) + 98 = 98 (million dollars)
