can you solve this linear programing problem?
Question by Troy R: can you solve this linear programing problem?
A man raises chickens, ducks and turkeys. He has room for only 200 birds and wishes to limit the number of turkeys to a maximum of P25, the number of turkeys and ducks to a maximum of P 100. His estimated profits are P30, P25, and P 120 on each chicken, duck, and turkey respectively. How many of each should he raise to maximize his profit?
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One Response to can you solve this linear programing problem?
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Let x1, x2, x3 are numbers of chickens, ducks and turkeys respectively. Then we”ll have the following problem:
Profit = 30*x1 +25*x2 + 120*x3 – to be maximized;
Constraints:
x1 + x2 + x3 ≤ 200;
0 ≤ x1 ≤ 100; /I suppose You have a misprint here, You’ve meant chickens instead of turkeys/
0 ≤ x2 ≤ 100;
0 ≤ x3 ≤ 25;
I solved it with a simplex-method on my computer and obtained the optimal solution:
x1 = 100 (chicks); x2 = 75 (ducks); x3 = 25 (turkeys);
maximum profit = 7875.
Duke
March 21, 2013 at 3:33 pm