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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(r + y)². 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 I> 2(y – 1). 1. Does P have critical points?

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(r + y)². 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 I> 2(y – 1). 1. Does P have critical points?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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.
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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