Simplex Method problem

I'm having problems solving this one: Use the Simplex Method. Maximize P = 2x1 + 8x2 + 10x3 +x4 Subject to the constraints x1 + 2x2 + x3 +x4  50 3x1 + x2 + 2x3 +x4  100 x1 >0, x2 >0, x3 >0, x4 >0

method incorporating the duality

Minimize C = 4x1 + 2x2 Subject to the constraints x1 + 2x2 >4 x1 + 4x2 >6 x1 >0, x2 >0 Use the method incorporating the duality.

maximum profit

A brewery manufactures 3 types of beer ---lite, regular and dark. Each vat of lite beer requires 6 bags of barley, 1 bag of sugar, and 1 bag of hops. Each vat of regular beer requires 4 bags of barley, 3 bags of sugar, and 1 bag of hops. Each vat of dark beer requires 2 bags of barley, 2 bags of sugar, and 4 bags of hops. Each day the brewery has 800 bags of barley, 600 bags of sugar, and 300 bags of hops available. The brewery realizes a profit of $10 per vat of lite beer, $20 per vat of regular beer, and $30 per vat of dark beer. How many vats of lite, regular and dark beer should be brewed in order to maximize profits? What is the maximum profit?

Compound Interest

This is my problem: A man has $50,000 invested at 12% compounded quarterly at the time he retires. If he wishes to withdraw money every 3 months, for the next 7 years, what will be the size of his withdrawals?

Sinking Fund

$6000 is borrowed at 10% compounded semi-annually. The amount is to be paid back in 5 years. If a sinking fund is established to repay the loan sand interest in 5 years, and the fund earns 8% compounded quarterly, how much will have to be paid into the fund every 3 months?