Exercise III: Maximizing profit I Assume that a company gets r tons of steel from one provider, and y tons from another one. Assume that the profit made is then given by the function P(r, y) = 9r + 8y– 6(x + y)*. The first provider can provide at most 5 tons, and the second one at most 3 tons. Finally, in order not to antagonize the first provider, it was felt it should not provide to0 small a fraction, so that r 2 2(y – 1). 1. Does P have critical points? 2. Draw the domain of P in the ry-plane. 3. Describe each boundary in terms of only one variable, and give the corresponding range of that variable, for instance "“(r, r²) for r E [1,2]". There can be different choices.
Exercise III: Maximizing profit I Assume that a company gets r tons of steel from one provider, and y tons from another one. Assume that the profit made is then given by the function P(r, y) = 9r + 8y– 6(x + y)*. The first provider can provide at most 5 tons, and the second one at most 3 tons. Finally, in order not to antagonize the first provider, it was felt it should not provide to0 small a fraction, so that r 2 2(y – 1). 1. Does P have critical points? 2. Draw the domain of P in the ry-plane. 3. Describe each boundary in terms of only one variable, and give the corresponding range of that variable, for instance "“(r, r²) for r E [1,2]". There can be different choices.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![Exercise III: Maximizing profit I
Assume that a company gets r tons of steel from one provider, and y tons from another
one. Assume that the profit made is then given by the function
P(r, y) = 9x + 8y – 6(x + y).
The first provider can provide at most 5 tons, and the second one at most 3 tons. Finally,
in order not to antagonize the first provider, it was felt it should not provide too small a
fraction, so that r > 2(y – 1).
1. Does P have critical points?
2. Draw the domain of P in the ry-plane.
3. Describe each boundary in terms of only one variable, and give the corresponding
range of that variable, for instance "(r, r²) for r E [1,2]". There can be different
choices.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc06c13df-a186-457e-b92c-2ec76adcc88e%2F15028f21-77c8-45bd-a16a-49b8f21b11e8%2F07u6e4_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise III: Maximizing profit I
Assume that a company gets r tons of steel from one provider, and y tons from another
one. Assume that the profit made is then given by the function
P(r, y) = 9x + 8y – 6(x + y).
The first provider can provide at most 5 tons, and the second one at most 3 tons. Finally,
in order not to antagonize the first provider, it was felt it should not provide too small a
fraction, so that r > 2(y – 1).
1. Does P have critical points?
2. Draw the domain of P in the ry-plane.
3. Describe each boundary in terms of only one variable, and give the corresponding
range of that variable, for instance "(r, r²) for r E [1,2]". There can be different
choices.
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