1. A gardener has two fertilizers that contain different concentrations of nitrogen. One is 3% nitrogen and the other is 11% nitrogen. How many kg of each should he mix to obtain 20kg of a 9% concentration ?
2.A company has taxable income of $ 312,000. The federal tax is 25% of that portion left after the state tax has been paid. The state tax is 10% of that portion after the federal tax has been paid. Find the federal and state taxes ?
3.Suppose a manufacturers production function is given by
16q=65-4(L-4)^2 - 2(k-5)^2
and the cost to the manufacturer is $ 8 per unit of labour and $ 16 per unit of capital, so that the total cost (in $) is 8L+16k. The selling price of the product is $ 64 per unit.
a) express the profit as a function of L and k. Give your answer in expanded form.
b) Find all critical points of the profit function obtained in part (a). Apply the second derivative test at each critical point. if the point is relative maximum, compute the corresponding relative maximum profit.
c) The profit may be considered as a function of L,k, and q subject to the constraint
16q=65-4(L-4)^2 - 2(k-5)^2
i) express the profit P as a function of L,k and q.
ii) use the method of Lagrange multipliers to find all critical points of P, the profit, subject to the constraint.
Thank You Very Much....
Im really appreciate...
2.A company has taxable income of $ 312,000. The federal tax is 25% of that portion left after the state tax has been paid. The state tax is 10% of that portion after the federal tax has been paid. Find the federal and state taxes ?
3.Suppose a manufacturers production function is given by
16q=65-4(L-4)^2 - 2(k-5)^2
and the cost to the manufacturer is $ 8 per unit of labour and $ 16 per unit of capital, so that the total cost (in $) is 8L+16k. The selling price of the product is $ 64 per unit.
a) express the profit as a function of L and k. Give your answer in expanded form.
b) Find all critical points of the profit function obtained in part (a). Apply the second derivative test at each critical point. if the point is relative maximum, compute the corresponding relative maximum profit.
c) The profit may be considered as a function of L,k, and q subject to the constraint
16q=65-4(L-4)^2 - 2(k-5)^2
i) express the profit P as a function of L,k and q.
ii) use the method of Lagrange multipliers to find all critical points of P, the profit, subject to the constraint.
Thank You Very Much....
Im really appreciate...