Write a computer code to perform the gradient method of steepest ascent algorithm using the multiplier technique λk+1 =₰ λ_k discussed in this section. Use your code to solve Problems 1, 5, 6, and 7 of this section.

Data from problem 1

Find the local maximum value of the function:

Data from problem 5

A company manufactures x floor lamps and y table lamps each day. The profit in dollars for the manufacture and sale of these lamps is:

Data from problem 6

If x and y are the amounts of labor and capital, respectively, to produce:

Data from problem 7

The total cost to manufacture one unit of product A is $3, and for one unit of product B it is $2. If x and y are the retail prices per unit of A and B, respectively, then marketing research has established that:

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f(x, y) = xy - x - y - 2x - 2y + 4