A small company has an assembly line that produces three typ

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 300 widgets that may be sold for a total of $3700. Find the quantity of each type of widget produced on a day when the number of basic widgets and top-of-the-line widgets is the same.

Solution

Let x be no. of $10 per unit for basic widget

y be no. of $ 12 per unit for mid line widegt

z be no. of $ 15 per unit for top of line widget

So, total no. of widgets = 300

So, x+y +z = 300 ----(1)

Total sale = $ 3700

10x +12y +15z = 3700 ----(2)

Given : x= z ----(3)

Using substitution to solve the equations:

x+y +x = 300---> 2x +y = 300 ---(3)

10x+12y +15x = 3700 ---->25x +12y = 3700 ---(4)

Multiplying equation 3 by 12

24x +12y = 3600

25x +12y = 3700

------------------------(subtract)

x = 100

z= 100

y = 200