1. Solve the following linear programming problem using the corner point method:
Maximize 3 X + 5Y
Subject to: 4X + 4Y 48
1X + 2Y 20
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.
The solution uses the corner point method in the linear programming problem.