Quadratics Jeans

Question

 

A manufactor of brand A jeans has a daily production costs of

C = 0.3x^{2 _} 120x+12,575where C is the total cost ( in dollars) and x is the number of jeans produced. How many jeans should be produced each day in order to minimize  costs? 

what is the mininum daily cost 

^{the manu should produce ___ jeans each day to minimize costs?} 

Answer 1

With any quadratic, the vertex is the maximum or minimum point.  If a quadratic is in the form ax² + bx +c, then the vertex occurs at x = -b/2a.

 

So, in this problem, a = 0.3 and b = -120, so the maximum happens when x = -(-120)/(2*0.3) = 120/0.6 = 200.

When 200 jeans are produced the cost will be minimized.

 

To determine that cost, just plug 200 into the formula.

C = 0.3(200)² - 120(200) + 12,575 = 12000 - 24000 + 12575 = $575 per day.