SOLUTION: Business. A small company has an assembly line that produces three types of widgets. The basic widget is sold for $10 per unit, the midprice widget for $12 per unit, and the top

Algebra ->  Statistics  -> Linear-regression -> SOLUTION: Business. A small company has an assembly line that produces three types of widgets. The basic widget is sold for $10 per unit, the midprice widget for $12 per unit, and the top      Log On


   

Question 1161446: Business. A small company has an assembly line that
produces three types of widgets. The basic widget is sold for
$10 per unit, the midprice widget for $12 per unit, and the
top-of-the-line widget for $15 per unit. The assembly line
has a daily capacity of producing 325 widgets that may be
sold for a total of $3825. Find the quantity of each type of
widget produced on a day when twice as many basic widgets
as top-of-the-line widgets are produced.
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the number of the top-of-the-line widgets.


Then the number of the basic widgets is 2x, according to the condition,

and the rest  (325-x-2x) = (325-3x)  widgets are mid-price.


Then the total revenue equation is


    10*(2x) + 12*(325-3x) + 15x = 3825   dollars.


From the equation,

    x = %283825-12%2A325%29%2F%2820-+36+%2B+15%29 = 75.


ANSWER.  75 top-of-the-line widgets;  2*75 = 150 basic widgets; and the rest (325 - 75 - 150) = 100  are mid-price widgets.

Solved // using one single equation in one unknown (!)