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Linear Programming:
Carpentry: Emilio has a small carpentry shop where he makes large and small bookcases. His profit on a large bookcase is $80 and on a small book case it is $50. It takes Emilio 6 hours to make a large bookcase and 2 hours to make a small one. He can spend only 24 hours each week on his carpentry work. He must make at least two of each size each week. What is the maximum weekly profit?

Respuesta :

nobillionaireNobley
Let the number of large bookcases be x and number of small bookcases be y, then
Maximise P = 80x + 50y;
subkect to:
6x + 2y ≤ 24
x, y ≥ 2

The corner points are (2, 2), (2, 6), (3.333, 2)
For (2, 2): P = 80(2) + 50(2) = 160 + 100 = 260
For (2, 6): P = 80(2) + 50(6) = 160 + 300 = 460
For (3.333, 2): P = 80(3.333) + 50(2) = 266.67 + 100 = 366.67

Therefore, for maximum profit, he should produce 2 large bookcases and 6 small bookcases.

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