set up of equation under three problem solving

Question

A manufacturing firm produces three poducts,A,Band C.The fixed cost is 170000 ghanan cedis per period and the cost of producing each units of A,B andC are 70,50,and 40 ghana cedis respectively. The sales and marketing department has estimated that profits for each units sold of A,B,and C are 30,20, and10 ghana cedis respectively. In the last period, a total of 11000units of all three products which were produced and sold realised a total profit of 250000 ghana cedis. The total cost incurred by the firm for producing all the three products in that period was 800000 ghana cedis.

a,set up the linear system of equations that can be solved simultaneously for each units the products in that was produced last period.

b,find the numer of units of each product produced last period by solving the linear system obtained in a above

Answer 1

Let A=number of product A, B=number of product B, C=number of product C.

Variable cost of production=70A+50B+40C; Fixed cost=170000.

Total cost=800000=170000+70A+50B+40C.

So, 70A+50B+40C=630000 which can be written 7A+5B+4C=63000. Call this equation (1).

Total product=11000=A+B+C. Call this equation (2).

Profit=250000=30A+20B+10C, so 3A+2B+C=25000. Call this equation (3).

PART a: The 3 equations are (1), (2) and (3) as defined above.

PART b. Now we can solve the equations.

(4)=(3)-(2): 2A+B=14000 (This means equation (4) is the result of subtracting equation (2) from equation (3))

Similarly:

(5)=(1)-4(2): 3A+B=19000

(6)=(5)-(4): A=5000, so B=14000-2A=14000-10000=4000, and C=11000-(A+B)=2000.