Melissa Bakery is preparing for the coming thanksgiving festival. The bakery plans to bake and sell its favourite cookies; butter cookies, chocolate cookies and almond cookies. A kilogram of butter cookies requires three cups of flour, one cup each of special ingredient and choc chip. A cup of special ingredient is added to five cups of flour together with three cups of choc chic to bake a kilogram of chocolate cookies. For baking a kilogram of almond cookies; Melissa requires four cups of flour, a cup of special ingredient and two cups of choc chip. However, each day the bakery can only allocate at most 400 cups of flour, 100 cups of special ingredient and 210 cups of choc chip to bake the cookies. Melissa estimates a daily profit of RM10 for butter cookies, RM20 for chocolate cookies and RM15 for almond cookies. The bakery wishes to maximize the daily profit.
a. Formulate the given problem as a linear programming problem?
b. The following is the final simplex tableau for the above problem:
|
Cj
|
|
10
|
20
|
15
|
0
|
0
|
0
|
|
|
|
Solution Mix
|
x1
|
x2
|
x3
|
S1
|
S2
|
S3
|
Quantity
|
|
10
|
x1
|
1
|
0
|
1/2
|
3/4
|
0
|
0
|
37.5
|
|
0
|
S2
|
0
|
-2/3
|
0
|
½
|
0
|
-1
|
5
|
|
20
|
x2
|
0
|
1
|
1/2
|
¼
|
0
|
1/3
|
57.5
|
|
|
Zj
|
10
|
20
|
15
|
25/2
|
0
|
20/3
|
m
|
|
|
Cj-Zj
|
0
|
0
|
0
|
-25/3
|
0
|
-20/3
|
|
i. Set up the initial simplex tableau for the above problem
ii. How many kilograms of each cookie should be baked?
iii. Determine the value of m
iv. Identify any ingredient that is not fully utilized. State the amount unused.
v. How would the optimum solution change if the RHS value for the first resource increases by 10 units?