Question 1191132: A manufacturer produces three products, A, B, and C. The profits for each unit of A, B, and C sold are $1, $2, and $3, respectively. Fixed costs are $19000 per year, and the costs of producing each unit of A, B, and C are $4, $5, and $7, respectively. Next year, a total of 11,000 units of all three products is to be produced and sold, and a total profit of $25,000 is to be realized. If total cost is to be $82,000, how many units of each of the products should be produced next year?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x is the number of units of product A.
y is the number of units of product B.
z is the number of units of product C
your objective function is:
profit = 1x + 2y + 3z = 25000
costs = 19000 + 4x + 5y + 7z = 82000
number of units to be produced and sold = x + y + z = 11000
you have 3 equations that need to be solved simultaneously.
they are:
1x + 2y + 3z = 25000
19000 + 4x + 5y + 7z = 82000
x + y + z = 11000
after solving these 3 equations simultaneously, you get:
x = 2000
y = 4000
z = 5000
1x + 2y + 3z = 2000 + 8000 + 15000 = 25000
19000 + 4x + 5y + 7z = 19000 + 8000 + 20000 + 35000 = 82000
x + y + z = 2000 + 4000 + 5000 = 11000
this confirms the solution is correct.
the solution is:
2000 units of product A and 4000 units of product B and 5000 units of product C need to be produced and sold to get a profit of 25000 at a total cost of 82000.
if you need to know to solve the 3 equations simultaneously, let me know and i'll go through it with you.
let me know if you have any other questions or concerns as well.
theo
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