QUESTION 2 a) b) Ferrero Candy Company makes three types of candy, which are solid, fruit and cream- filled and packages these candies in three assortments. A box of assortment I contains 4 solids, 4 fruits and 12 creams. While, a box of assortment II contains 12 solids, 4 fruits and 4 creams. Lastly, a box of assortment III contains 8 solids, 8 fruits and 8 creams. The company can manufacture up to 4800 solids, 4000 fruits and 5600 cream candies weekly. The profit of each box of assortment I, II and III are RM4, RM3 and RM5 respectively. The company wishes to maximize its profit. Formulate the problem as a linear programming model. A manufacturing company produces three types of products (R, S and T). The following is an incomplete final simplex tableau for a linear programming maximization problem. X₁, X2 and X3 represents the units of products R, S and T, respectively. S₁, S₂ and S3 are the slack variables for Resources 1, 2 and 3, respectively. Cj i. ii. S₁ 0 1/8 -1/16 0 1/16 -1/16 Find the values of A, B and C in the above simplex tableau. A 5 4 Basic X₂ X3 X₁ Zj Cj-Zj X₁ 4 lo 0 1 4 0 State the optimal solution. X₂ 3 1 OI 0 OWO 3 iii. Which resources are fully utilized? X3 5 0 1 0 5 0 S₂ 0 -1/8 1/4 -1/8 3/8 B S3 0 v. Write the dual solution for the above problem and interpret. 0 -1/16 1/8 3/16 -3/16 iv. If Resource 2 is increased by 10 units, how much will the new profit be? RHS 100 350 200 C
QUESTION 2 a) b) Ferrero Candy Company makes three types of candy, which are solid, fruit and cream- filled and packages these candies in three assortments. A box of assortment I contains 4 solids, 4 fruits and 12 creams. While, a box of assortment II contains 12 solids, 4 fruits and 4 creams. Lastly, a box of assortment III contains 8 solids, 8 fruits and 8 creams. The company can manufacture up to 4800 solids, 4000 fruits and 5600 cream candies weekly. The profit of each box of assortment I, II and III are RM4, RM3 and RM5 respectively. The company wishes to maximize its profit. Formulate the problem as a linear programming model. A manufacturing company produces three types of products (R, S and T). The following is an incomplete final simplex tableau for a linear programming maximization problem. X₁, X2 and X3 represents the units of products R, S and T, respectively. S₁, S₂ and S3 are the slack variables for Resources 1, 2 and 3, respectively. Cj i. ii. S₁ 0 1/8 -1/16 0 1/16 -1/16 Find the values of A, B and C in the above simplex tableau. A 5 4 Basic X₂ X3 X₁ Zj Cj-Zj X₁ 4 lo 0 1 4 0 State the optimal solution. X₂ 3 1 OI 0 OWO 3 iii. Which resources are fully utilized? X3 5 0 1 0 5 0 S₂ 0 -1/8 1/4 -1/8 3/8 B S3 0 v. Write the dual solution for the above problem and interpret. 0 -1/16 1/8 3/16 -3/16 iv. If Resource 2 is increased by 10 units, how much will the new profit be? RHS 100 350 200 C
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 56P
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Transcribed Image Text:QUESTION 2
a)
b)
Ferrero Candy Company makes three types of candy, which are solid, fruit and cream-
filled and packages these candies in three assortments. A box of assortment I contains
4 solids, 4 fruits and 12 creams. While, a box of assortment II contains 12 solids, 4
fruits and 4 creams. Lastly, a box of assortment III contains 8 solids, 8 fruits and 8
creams. The company can manufacture up to 4800 solids, 4000 fruits and 5600 cream
candies weekly. The profit each box of assortment I, II and III are RM4, RM3 and
RM5 respectively. The company wishes to maximize its profit.
Formulate the problem as a linear programming model.
A manufacturing company produces three types of products (R, S and T). The following
is an incomplete final simplex tableau for a linear programming maximization problem.
X₁, X₂ and X3 represents the units of products R, S and T, respectively. S₁, S2 and S3
are the slack variables for Resources 1, 2 and 3, respectively.
i.
ii.
A
5
4
Basic
X₂
X3
X₁
Zj
Cj-Zj
X₁
4
0
O
1
4
0
X₂
3
1
0
O
3
0
State the optimal solution.
X3
5
iii. Which resources are fully utilized?
OTOSO
1
0
5
0
S₁
0
1/8 -1/8
1/4
-1/16
0
1/16
-1/16
S₂
0
Find the values of A, B and C in the above simplex tableau.
-1/8
3/8
B
S3
0
v. Write the dual solution for the above problem and interpret.
0
-1/16
1/8
3/16
-3/16
iv. If Resource 2 is increased by 10 units, how much will the new profit be?
RHS
100
350
200
C
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