7.A manufacturer’s production is modeled by the cobb‐Douglas function
f(x,y)=
Where x represents the units of labor ( at $ 150 per unit ) and y represents the units of capital ( at $ 250 per unit ). The total cost for labor and capital cannot exceed $ 50,000. Will the manufacturer’s maximum production level exceed 16,000 units? ( Hint: Use the method of Lagrange Multipliers and the funciton . F(x,y,λ)=f(x,y)-λ(150x+250y-50,000).)
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