A company produces 3 different products A B and C The cost o

A company produces 3 different products: A, B. and C. The cost of producing each unit of A, B, and C is $2, $3, and $4 respectively. The profit for each unit of A, B, and C sold is $1, $2, and $4 respectively. If the company is planning to produce and sell a total of 40,000 units of all three products, and it is expecting a total profit of $96,000. with a total cost of $123,000 for production, how many units of each product should be produced?

Solution

Given A,B,C are 3 different products.

Producing cost of each product is $2, $3, $4

Profit of each product is $1, $2, $4

Toal produced products of A,B,C together is 40,000

Total producing cost = $123,000

Total profit = $96,000

Need to find the units of products produced

Let Product A of X units,  Product B of Y units,  Product C of Z units.

Then equation for total units of production is X+Y+Z=40,000

Equation for producing cost is 2X+3Y+4Z=123,000

Equation for total cost is X+2Y+4Z=96,000

Solving for X,Y and Z:

X+Y+Z=40,000   2X+3Y+4Z=123,000 X+2Y+4Z=96,000

Subtract equation3 from equation2 :  2X+3Y+4Z-(X+2Y+4Z)=123,000-96,000

X+Y=27,000

Substitute X+Y=27,000 in equation1 : X+Y+Z=40,000

27,000+Z=40,000

Z=40,000-27,000

Z=13,000

Subtract equation1 from equation3 : X+2Y+4Z-(X+Y+Z)=96,000-40,000

Y+3Z=56,000

Substitute Z: Y+3(13,000)=56,000

Y+39,000=56,000

Y=56,000-39,000

Y=17,000

Substitute X and Z in equation1 : X+Y+Z=40,000

X+17,000+13,000=40,000

X+30,000=40,000

X=40,000-30,000

  X=10,000

Therefore, X=10,000, Y=17,000, Z=13,000

Product A is of 10,000 units, Product B is of 17,000 units, Product C is of 13,000 units.