A factory that makes statues is trying to maximize its income. Their two primary products are the Liberty and David statues. Each Liberty requires 18 minutes of machine time to rough cut the shape and 36 minutes of artist time to finish the details. The David requires 27 minutes on the machines and 18 minutes with the artist's hand. The factory is limited each day to 162 minutes of machine time and 216 minutes of artist time. Both use 7 pounds of stone, and the factory has 49 pounds of stone available per day. If each Liberty brings in a profit of sixty-three dollars, and each David brings in ninety-six dollars, how many statues of each type should the factory make each day?

Constraints:
⎧
⎪
⎨
⎪
⎩
18
L
+
27
D
≤
162
36
L
+
18
D
≤
216
7
L
+
7
D
≤
49

Objective:
Income =
63
L
+
96
D

Question

31-10-2021
Mathematics

Answered

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A factory that makes statues is trying to maximize its income. Their two primary products are the Liberty and David statues. Each Liberty requires 18 minutes of machine time to rough cut the shape and 36 minutes of artist time to finish the details. The David requires 27 minutes on the machines and 18 minutes with the artist's hand. The factory is limited each day to 162 minutes of machine time and 216 minutes of artist time. Both use 7 pounds of stone, and the factory has 49 pounds of stone available per day. If each Liberty brings in a profit of sixty-three dollars, and each David brings in ninety-six dollars, how many statues of each type should the factory make each day?

Constraints:
⎧
⎪
⎨
⎪
⎩
18
L
+
27
D
≤
162
36
L
+
18
D
≤
216
7
L
+
7
D
≤
49

Objective:
Income =
63
L
+
96
D

Sagot :

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