SOLUTION: A charity worker is going to sell wigs, candles and hat clips to raise funds for their organization. The cost a wig for $10 and sell it at the price of $30, the cost of a candle is

Question 1194099: A charity worker is going to sell wigs, candles and hat clips to raise funds for their organization. The cost a wig for $10 and sell it at the price of $30, the cost of a candle is $ 4 and they sell them for $ 12 and the hat clips cost $ 10 and sell them for $24. They have the maximum budget to buy the stuff is $ 4000. the area of a table is 60" long and 30" wide. The area occupied by the wigs is 10square inch, the candle occupied 6square inch and the hat clips 2 square inch. How should the charity organize their stuff so they can get the maximum profit?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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See the solution given by Edwin at this link

https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1194100.html

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Below is the solution which uses free of charge online solver from the Internet for the simplex method.

Let x = # of wigs;  y = # of candles and z = # of the hat clips.


The problem is to maximize the profit function

    P(x, y, z) = 20x + 8y + 14z


under these restrictions

    10x + 4y + 10z <= 4000,

    10x + 6y +  2z <= 1800.


Now go to the site https://www.zweigmedia.com/RealWorld/simplex.html

and use free of charge solver there.


Input the profit function and the restrictions and press the "Solve" button.


It will solve this maximization problem using the "simplex method".


The solver produces this solution (this answer)


   x = 175 wigs;  y = 0 candles;  z = 275 hat clips;  p = $6350.    ANSWER

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The input to the solver is shown/presented/documented below :

Maximize p = 20x + 8y + 14z subject to
10x   +   4y   +  10z    <= 4000 
10x   +   6y   +   2z    <= 1800
x >= 0  
y >= 0
z >= 0

Solved.

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