1. Solve the following linear programming problem using the corner point method:

Maximize 3 X + 5Y

Subject to: 4X + 4Y 48

1X + 2Y 20

Y 2

X, Y 0

2. The Fido Dog Food Company wishes to introduce a new brand of dog biscuits (composed of chicken and liver-flavored biscuits) that meets certain nutritional requirements. The liver-flavored biscuits contain 1 unit of nutrient A and 2 units of nutrient B, while the chicken-flavored ones contain 1 unit of nutrient A and 4 units of nutrient B. According to federal requirements, there must be at least 40 units of nutrient A and 60 units of nutrient B in a package of the new mix. In addition, the company has decided that there can be no more than 15 liver-flavored biscuits in a package. If it costs 1 cent to make a liver-flavored biscuit and 2 cents to make a chicken-flavored one, what is the optimal product mix for a package of the biscuits in order to minimize the firm's cost?

(a) Formulate this as a linear programming problem.

(b) Find the optimal solution for this problem graphically

(c) Are any constraints redundant? If so, which one or ones?

(d) What is the total cost of a package of dog biscuits using the optimal mix?

3. Consider the following linear programming problem:

Maximize : 10X + 30Y

Subject to : X + 2Y ? 80

8X + 16Y ? 640

4X + 2Y ? 100

X, Y ? 0

This is a special case of a linear programming problem in which

(a) there is no feasible solution.

(b) there is a redundant constraint.

(c) there are multiple optimal solutions.

(d) this cannot be solved graphically.

(e) none of the above