1. Tan has 551 dollars to spend on two goods, good 1 and good 2. Let x₁ and x₂ denote respectively the quantity of good 1 and the quantity of good 2. The price of good 1 is 3.7 and the price of good 2 is 10. What is the absolute value of theslope (dx₂/dx₁) of Tan's budget lineat the point where x₁= 6.8?

2. Tom has 500 dollars to spend on two goods, good 1 and good 2. The seller of good 1 offers Tom the following deal:

For every three units (of good 1) you buy, you will get the fourth unit for free.

Determine how many units of good 1 Tom will end up with if the price of good 1 is 3, the price of good 2 is 8, Tom spends all his income on the two goods and buys 9 units of good 2.

3. Tan has 170.4 dollars to spend on two goods, good 1 and good 2. Let x₁ and x₂ denote respectively the quantity of good 1 and the quantity of good 2. The price of good 1 is 9.1 and the price of good 2 is 5.4. Suppose that the government subsidizes all consumers of good 2 by 2 dollars per unit on every unit of good 2 each person buys but only if the amount of good 2 exceeds 10 units. If Tan buys x₁= 6.5 units of good 1,what is the maximum amount of good she can buy?