The amount of space required by a particular firm is given below, where x and y

Question

The amount of space required by a particular firm is given below, where x and y are, respectively, the number of units of labor and capital utilized. f(x,y) = 1000 sqrt(6x^2 + y^2) Suppose that labor costs $480 per unit and capital costs $40 per unit and that the firm has $8000 to spend. Determine the amounts of labor and capital that should be utilized in order to minimize the amount of space required. (Hint: To minimize f(x, y) it is enough to minimize the function 6x2 + y2.)

a) _____ units of labor

b) _____ units of capital

Explanation / Answer

a) __25___ units of labor

b) ____16_ units of capital

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