Math Question

Question

IN a given day mill turns out twice as many units of plywood as lumber. It makes profit of 30 dollars on a unit of lumber abd 40 dollars on a unit of plywood.How many of each unit must be produced and sold i order to make a profit of 11440

Answer 1

 

Let P = units of plywood

Let L = units of lumber

 

Since the mill turns out twice as many units of plywood as lumber,

 

    P = 2L      (Equation 1)

 

The profit from each unit of plywood is 40, and the profit from each unit of lumber is 30.  the total profit is 11440.

 

   30L + 40P = 11440        (Equation)

 

Substituting equation 1 into equation 2 ..... P = 2L

 

   30L + 40P = 11440

   30L + 40(2L) = 11440

   30L + 80L = 11440

   110L = 11440

   L = 11440/110

   L = 104

 

Since P = 2L

 

   P = 2(104) = 208

 

In order to produce a profit of 11,440 the mill needs to produce

    104 units of lumber and

    208 units of plywood

 

CHECK:

   30(L) =  30(104) = 3120

 

   40(P) = 40(208) = 8320

 

   3120 + 8420 = 11440