Problem 1: The processing division of the Sunrise Breakfast Company must produce one ton (2000 pounds) of breakfast flakes per day to meet the demand for its Sugar Sweet cereal. Cost per pound of the three ingredients is:
Ingredient A: $4 per pound
Ingredient B: $3 per pound
Ingredient C: $2 per pound
Government regulations require that the mix contain at least 10% ingredient A and 20% ingredient B. Use of more than 800 pounds per ton of ingredient C produces an unacceptable taste.
Determine the minimum-cost mixture that satisfies the daily demand for Sugar Sweet. Can the bounded variable simplex method used to solve this problem?
Problem 2: The table given below corresponds to maximization problem in decision variables xj ≥ 0 (j = 1, 2, ... , 5):
|
Basic Variable
|
Current Value
|
x1
|
x2
|
x3
|
x4
|
x5
|
|
x3
|
4
|
-1
|
a1
|
1
|
|
|
|
x4
|
1
|
a2
|
-4
|
|
1
|
|
|
x5
|
b
|
a3
|
3
|
|
|
1
|
|
(- z)
|
-10
|
c
|
-2
|
|
|
|
State condition on all five unknown's a1, a2, a3, b and c, such that the following statements are true.
a. The current solution is optimal. There are multiple optimal solutions.
b. The problem is unbounded
c. The problem is infeasible.
d. The current solution is not optimal (assume that b ≥ 0). Indicate the variable that enters the basis, the variable that leaves the basis, and what the total change in profit would be for one iteration of the simplex method for all values of the unknown that are not optimal.