Question 1189977
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Hello,
I have some problems with this task, could you help me make formulas 
to be able to solve the task? The results are not that important for me, a clear solution would be great.


A western shop wishes to purchase 470 felt and 370 straw cowboy hats. 
Bids have been received from three wholesalers. 
Texas hatters has agreed to supply not more than 370, 
Lone Star Hatters not more than 463, and Lariat Ranch Wear not more than 185. 
The owner of the shop has estimated that his profit per hat sold 
from Texas Hatters would be $3/felt and $4/straw, 
from Lone Star Hatters would be $3,80/felt and $3,50/straw and 
from Lariat Ranch Wear $4/felt and $3,60/straw. 
Solve this to maximize the owner's profit, and calculate that profit.
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<pre>
To present information in compact form, I prepared this table 


      T       A         B         L          E


             Texas    Lone    Lariat    To purchase
  
    felt       3      3.80      4          470

    cowboy     4      3.50      3.60       370

    maximum   370     463       185



Now imagine that you are agressive buyer/seller, who wants to get maximum profit.


You look at the table, and you see that among felt hats, you will get maximum profit of $4/hat from Lariat.
So you take as many felt hats as possible from Lariat: 185.

    After that, you still need 470-185 = 285 felt hats.


You look at the Table again, and you see that next the most profitable felt hat is from Lone at $3.80 -
so you buy these 285 felt hats from Lone: the Lone's restriction of 463 hats allows you to do it.


    At this point, you completed with felt hats and provided a profit of 185*4 + 285*3.80 = 1823 dollars.

    Next, we will work/analyze/buy cowboy hats.



You look at the table again, and you see that among cowboy hats, you will get maximum profit of $4/hat from Texas.
So you take as many cowboy hats as possible from Texas: 370.

    After that, you just completed with the cowboy hats and provided your profit of 370*4 = 1480 dollars.


RESUME: you buy 185 felt hats from Lariat and 285 felt hats from Lone;

        you buy 370 cowboy hats from Texas.

        Doing this way, you provide total profit of 1823 + 1480 = 3303 dollars, and it is maximum possible 
            (OPTIMUM) profit under imposed conditions.

</pre>

Solved.


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Thus you do not need formula/formulas or special software to solve this problem.


Only reasoning and common sense.  &nbsp;&nbsp;&nbsp;&nbsp;<<<---=== &nbsp;&nbsp;&nbsp;&nbsp;The given problem is &nbsp;SPECIALLY &nbsp;intended for it . . .