Business Calculus

Question

The production cost per week for producing 𝑥 widgets is given by, C(x) = 500 + 350x = 0.09x^2, where 0 ≤ x ≤ 1000.

Interpret the results of C(100) and C'(100), as well as using these results, estimate the cost of producing 101 widgets.

Answer 1

C(x) = 50 + 350x + 0.09x^2

C(100) = 50 + 350(100)+ 0.09(100)^2 = 50+ 35,000+ .09(10000)

= 35,050 + 900= 35,950

C'(x) = 350 + 0.18x

C'(100) = 350 + 0.18(100) = 350 + 18 = 368

C(101) = 50 + 350(101) + 0.09(101)^2 = 50 + 35,350 + 909 = 35,400+ 909 = 36,309

C(100)+C'(100) = 35,950 + 368 = 36,318 which is close to C(101), just 9 more.

C(100) is the cost of 100, C'(100) is the cost of one more, if the cost function were linear. For small x, it's almost linear.