Assume hedger takes hedge ratio as h*, i.e, if the risk exposure is a long position of 100 units of spot commodity, to hedge the risk, hedger will short 100h* futures underlying on that commodity.

c) To make the hedge portfolio risk-free, the value of the portfolio should not vary no matter stock price rises or falls (or, equivalently, the hedge portfolio should not make profit in one state and make loss in the other, where the state means stock price rises or falls). Please based on the above fact, solve the optimal hedge ratio h*. [1 mark]

d) To make the hedge portfolio risk-free, the hedge portfolio should not make profit in one state and make loss in the other, where the state means stock price rises or falls. Please use the optimal hedge ratio solved in (c) to verify this fact. [1 mark]

2) Should nonuniform policies in the EU (i.e., cherry picking EU policies that members may choose to follow) be tolerated or encouraged? Make your case.

The WorldLight Company produces two light fixtures (products 1 and 2) that require both metal frame parts and electrical components. Management wants to determine how many units of each product to produce so as to maximize profit. For each unit of product 1, 1 unit of frame parts and 2 units of electrical components are required. For each unit of product 2, 3 units of frame parts and 2 units of electrical components are required. The company has 200 units of frame parts and 300 units of electrical components. Each unit of product 1 gives a profit of €1, and each unit of product 2, up to 60 units, gives a profit of €2. Any excess over 60 units of product 2 brings no profit, so much excess has been ruled out.

(a) Formulate a linear programming model for this problem.
(b) Use the graphical method

You want to know if college students have more stress in their daily lives than the general population (μ = 12), so you gather data from 25 people to test your hypothesis. Your sample has an average stress score of X̅ = 13.11 and a standard deviation of s = 3.89. Use a 1-sample t-test to see if there is a difference.

a) The diagrams shown below are the result of executing an algorithm which has one parameter, N, which must be a non-negative integer, and alphabet boxes on a 10<10 grid. For values of N from O to 5, the algorithm produces the following patterns:

Equivalently, to make the hedge portfolio risk-free, the hedge portfolio should not make a profit in one state and make a loss in the other, where the state means stock price rises or falls. Please use the optimal hedge ratio solved in (c) to verify this fact.

Should non-uniformity policies in the EU (i.e.,cherry picking EU policies that members may choose to follow) be tolerated or encouraged? Make your case.