A bicycle manufacturer builds one-, three- and ten-speed models. The bicycles ne
ID: 3111008 • Letter: A
Question
A bicycle manufacturer builds one-, three- and ten-speed models. The bicycles need both aluminum and steel. The company has available 40, 940 units of steel and 52, 050 units of aluminum. The one-, three-, and ten-speed models need, respectively, 12, 16 and 20 units of steel and 20, 15, and 25 units of aluminum. How many of each type of bicycle should be made in order to maximize profit if the company makes $9 per one-speed bike, $12 per three-speed, and $30 per ten-speed. What is the maximum possible profit? Type the number of each type of bicycle that should be made. One-speed: 0 Three-speed: 0 Ten-speed: The maximum profit is $.Explanation / Answer
Solution:
let x unit of one model is needed
let y unit of three model is needed
let z unit of ten model is needed
using given condition
total steel consumed
10x + 16y + 20y <= 40940
total aluminum consumed
20x + 15y +25z =<52,050
to maximize the profit our objective function
p = 9x + 12y + 30z
usinig simplex method
Maximize p = 9x + 12y + 30z subject to
10x + 16y + 20z <= 40940
20x + 15y + 25z <= 52050
Tableau #1
x y z s1 s2 p
10 16 20 1 0 0 40940
20 15 25 0 1 0 52050
-9 -12 -30 0 0 1 0
Tableau #2
x y z s1 s2 p
0.5 0.8 1 0.05 0 0 2047
7.5 -5 0 -1.25 1 0 875
6 12 0 1.5 0 1 61410
from this table we conclude that
one speed x = 0,
three speed y= 0
ten speed z = 2047
the maximum profit is $ 61410
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