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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 :

MrRoyalidn

Optimizing function describes the minimum or maximum output from the function.

The factory should make 3 David statues and 4.5 Liberty statues

The constraints and the objective function are given as:

[tex]\mathbf{18L + 27 D \le 162}[/tex]

[tex]\mathbf{36L + 18 D\le 216}[/tex]

[tex]\mathbf{7L + 7D \le 49}[/tex]

[tex]\mathbf{Objective:\ Income = 63L+ 96D}[/tex]

We start by plotting the graphs of the inequalities, where L is represented on the vertical axis, and D on the horizontal axis

From the graph, the only optimal point is: D = 3 and L = 4.5

Hence, the factory should make 3 David statues and 4.5 Liberty statues

Read more about optimizing functions at:

https://brainly.com/question/11206462

View image MrRoyal
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