SOLUTION: Please help me to solve this problem. A manufacturer produces three products : A,B and C. the profit for each unit sold of A,B and C are $1,$2 and $3 , respectively. Fixed cost are

Question 462257: Please help me to solve this problem. A manufacturer produces three products : A,B and C. the profit for each unit sold of A,B and C are $1,$2 and $3 , respectively. Fixed cost are $17,000 per year and the cost 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 $80,000 , how many units of each of the products should be produced next year?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Please help me to solve this problem. A manufacturer produces three products : A,B and C. the profit for each unit sold of A,B and C are $1,$2 and $3 , respectively. Fixed cost are $17,000 per year and the cost 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 $80,000 , how many units of each of the products should be produced next year?
..
A+B+C=11000 (Total number of units to be produced and sold)
4A+5B+7C+17000=80000 (Total cost)
A+2B+3C=25000 (Profit)
We now have 3 equations with which we can solve for units of A, B, & C
..
1)A+B+C=11000
2)4A+5B+7C=63000
3)A+2B+3C=25000
subtract eq 1 fm eq 3
4)B+2C=14000
..
multiply eq 3 by 4
5)4A+8B+12C=100000
2)4A+5B+7C=63000
subtract eq 2 fm eq 5
6)3B+5C=37000
multiply eq 4 by 3
7)3B+6C=42000
subtract eq 6 fm 7
C=5000
solving for B
6)3B+5C=37000
3B+5(5000)=37000
3B=37000-25000=12000
B=4000
solving for A
1)A+B+C=11000
A+4000+5000=11000
A=11000-9000=2000
...
Check:
2)4A+5B+7C=63000
8000+20000+35000=63000 (check)
3)A+2B+3C=25000
2000+8000+15000=25000 (check)
..
Answers:
Units should be produced next year:
A=2000
B=4000
C=5000
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