|
Question 459574: Please help me solve this problem. A company manufactures products A and B. The cost of producing each unit of A is $2 more than that of B. The costs of production of A and B are $1500 and $1000, respectively, and 25 more units of A are produced than of B. How many of each are produced?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Please help me solve this problem. A company manufactures products A and B. The cost of producing each unit of A is $2 more than that of B. The costs of production of A and B are $1500 and $1000, respectively, and 25 more units of A are produced than of B. How many of each are produced?
..
let x=number of A units produced
x-25=number of B units produced
b=cost/B unit
b+2=cost/A unit
..
(b+2)x=1500
x=1500/(b+2)
..
b(x-25)=1000
b(1500/(b+2)-25)=1000
(1500/(b+2)-25)=1000/b
1500-25b-50=1000(b+2)/b
1500b-25b^2-50b=1000b+2000
-25b^2+450b-2000=0
25b^2-450b+2000=0
b^2-18+80=0
(b-8)(b-10)=0
b=8 (unit cost for B unit)
or 10 (reject, does not check)
(b+2)=10 (unit cost for A unit)
..
(b+2)x=1500
10x=1500
x=150 (A units produced)
x-25=125 (B units produced)
Ans:
A units produced=150
B units produced=125
|
|
|
| |
