Use the method of lagrange multipliers to find the maximum value of f(z, y) ay for positive values of x and y, subject to the constraint x + 4y = 12. 4. suppose that p(x, y) = 2x1/3y2/3 units of a product can be made using r units of labor and y units of capital. suppose that the cost per unit of labor is $16 and the cost per unit of capital is $4. use the method of lagrange multipliers to find the amounts z and y of labor and capital, respectively, that minimize the cost of producing 32 units of product. verify that for the values of r and y that minimize cost, 16

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answer: no, but if it does it's a obvious pattern.

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b: |12 – x| ≤ 0.25

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let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

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what is the model?

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