- #1

mrjericho1991

- 5

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1: A farm’s profit is given by π = 100x + 80y + 2xy− x(square) − 2y(square) − 5000, where x is the number of turkeys produced and ( is the number of beef cattle produced.

How many of each should be produced to maximise the profit?

Prove that profit is indeed maximised at this level of production?

What is the maximum profit?

2: A consumer’s utility function is given by U(x,y) = xy ( with the budgetary constraint 5x + 10y = 100.

Find the values of x and y ( that maximise the utility function, subject to the budgetary constraint.

What is the value of the Lagrange multiplier λ?