Exercise III: Maximizing profit I Assume that a company gets x tons of steel from one provider, and y tons from another one. Assume that the profit made is then given by the function P(x, y) = 9x + 8y – 6(x + 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 x > 2(y – 1). 1. Does P have critical points? 2. Draw the domain of P in the xy-plane. 3. Describe each boundary in terms of only one variable, and give the corresponding range of that variable, for instance "(x, x?) for x e [1,2]". There can be different choices. Exercise IV: Maximizing profit II Find the quantities that maximize the profit in Exercise III. Explain everything clearly.
Exercise III: Maximizing profit I Assume that a company gets x tons of steel from one provider, and y tons from another one. Assume that the profit made is then given by the function P(x, y) = 9x + 8y – 6(x + 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 x > 2(y – 1). 1. Does P have critical points? 2. Draw the domain of P in the xy-plane. 3. Describe each boundary in terms of only one variable, and give the corresponding range of that variable, for instance "(x, x?) for x e [1,2]". There can be different choices. Exercise IV: Maximizing profit II Find the quantities that maximize the profit in Exercise III. Explain everything clearly.
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Find the quantities that maximize the profit in Exercise III. Explain everything clearly.
*PLEASE ANSWER EXERCISE IV ONLY
![Exercise III: Maximizing profit I
Assume that a company gets x tons of steel from one provider, and y tons from another
one. Assume that the profit made is then given by the function
P(x, y) = 9x + 8y – 6(x + 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 x > 2(y – 1).
1. Does P have critical points?
2. Draw the domain of P in the xy-plane.
3. Describe each boundary in terms of only one variable, and give the corresponding
range of that variable, for instance "(x, x²) for x E [1, 2]". There can be different
choices.
Exercise IV: Maximizing profit II
Find the quantities that maximize the profit in Exercise III. Explain everything clearly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ebb6650-7cf6-48f7-a6e4-9d83df6ee4c3%2Fe433dda6-1d61-44e4-8701-7a7bae823017%2Fht4t4db_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise III: Maximizing profit I
Assume that a company gets x tons of steel from one provider, and y tons from another
one. Assume that the profit made is then given by the function
P(x, y) = 9x + 8y – 6(x + 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 x > 2(y – 1).
1. Does P have critical points?
2. Draw the domain of P in the xy-plane.
3. Describe each boundary in terms of only one variable, and give the corresponding
range of that variable, for instance "(x, x²) for x E [1, 2]". There can be different
choices.
Exercise IV: Maximizing profit II
Find the quantities that maximize the profit in Exercise III. Explain everything clearly.
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