Solution for Problem 1.3.3

Cost Equation:  Use the cost equation, C = 0.42x2 – 200x + 9,000, to find the number of units x that a manufacturer can produce for the cost C = $20,000.  Round to nearest integer.
We want to find the value(s) for x when   0.42x2 – 200x + 9,000 = 20,000

ax2 + bx + c = 0

Solve

Step

0.42x2 – 200x + 9,000 = 20,000

Original equation

0.42x2 – 200x – 11,000 = 0

Set equal to 0 by subtracting 20,000 from both sides.

a = 0.42, b = -200, c = -11,000

Identify coefficients

Substitute values for a, b , and c.  Then simplify.
There are 2 distinct answers.

Approximations...
x » (200 + 242)/ 0.84 » 526  
 x » (200 – 242)/ 0.84 » -50 must be positive

The cost to manufacture 526 units  is about $20,000

 C = 0.42(526)2 – 200(526) + 9,000 = 20,003.92