SOLUTION: A toy manufacturer produces two kind of toys T1 and T2. each toy has to go through 2 machines M1 and M2, and some handcraftsdone by the workers on every toy that is manufactured, t

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Question 1167639: A toy manufacturer produces two kind of toys T1 and T2. each toy has to go through 2 machines M1 and M2, and some handcraftsdone by the workers on every toy that is manufactured, toy T1 requires 3 hours in M1 and 8 hours in M2 with workers doing handcrafts on it for 4 hours. similarly toy T2 requires 5 hours in M1 and 3 hours in M2 with workers doing handcrafts on it for 9 hours. total time availible for M1 and M2 are 27 and 19 hours respectively with handcraft workers cannot work for more than 34 hours. if profit on selling toy T1 is 13$ and toy T2 in 25$. formulate the LP problem and find the maximum number of units of T1 and T2 that are to be manufactured.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i did this three ways.

first was graphically.
second was using the simplex method tool
third was using excel solver

all three agree on the solution.

the solution is:

x = 1.15, y = 3.266666...., max profit = 96.666666....

if an integer solution is necessary, then the solution is:

x = 1, y = 3, max profit = 88.

best to set up a table as shown below: 


                           T1        T2        requirement
                           x         y         
m1                         3         5         <= 27
m2                         8         3         <= 19
handcraft                  4         9         <= 34
profit                     13        25        maximize


here are the results from the graphical solution.



here are the results from the simplex method tool.



here are the results from the excel solver.



i don't have time to explain how i got these results right now, but i will be available tomorrow.

just let me know if you would like some further explanations as to the procedure for how any of these results were obtained.



Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.


I do not understand, why tutor @Theo solved problem maximizing the profit, while the post clearly

(or mistakenly ??) asks to maximize the number of units . . .


Also, I do not understand, for what reason a particular profits are given in the problem,
while the profit is not a subject of interest ?


Where are many aspects in this problem that go out of my understanding . . .