Solve question 2 using AMPL. Both mod and dat file are attached along with the calculated values from the files.

Question:

2. Is it worth increasing the supply of R1 beyond the present 500 units/day? The current supplier for R1 is unable to supply any more than the current amount. The procurement manager has identified a new supplier for R1, but that suppliers price is $15/unit higher than the current suppliers. Should additional supplies of R1 be ordered from this new supplier?

Table for context:

Solved values using MINOS 5.51:

objective = 32487.5

A = 200

B=587.5

C=787.5

D=662.5

E=400

F=0

G=0

mod file:

reset;

set P;

set Item;

param IO {Item, P};

param C {j in P};

param RHS {Item};

param l {j in P};

param u {j in P};

var x {j in P} >= 0;

maximize profit: sum {j in P} C[j]*x[j];

subject to MBEQ {i in Item}: sum {j in P} IO[i,j]*x[j]

limit {j in P}: l[j]

data project2.dat

solve;

dat file:

set P := A B C D E F G;

set Item := R1 R2 R3 P1 P2;

param IO default 0 :=

[R1,A] 0.1 [R1,B] 0.3 [R1,C] 0.2 [R1,D] 0.1

[R1,E] 0.2 [R1,F] 0.1 [R1,G] 0.2

[R2,A] 0.2 [R2,B] 0.1 [R2,C] 0.4 [R2,D] 0.2

[R2,E] 0.2 [R2,F] 0.3 [R2,G] 0.4

[R3,A] 0.2 [R3,B] 0.1 [R3,C] 0.1 [R3,D] 0.2

[R3,E] 0.1 [R3,F] 0.2 [R3,G] 0.3

[P1,A] 0.02 [P1,B] 0.03 [P1,C] 0.01 [P1,D] 0.04

[P1,E] 0.01 [P1,F] 0.02 [P1,G] 0.04

[P2,A] 0.04 [P2,C] 0.02 [P2,D] 0.02 [P2,E] 0.06

[P2,F] 0.03 [P2,G] 0.05;

param l default 0 :=

A 200;

param u default Infinity :=

B 800 E 400;

param RHS :=

R1 500 R2 750 R3 350 P1 60 P2 80;

param C:=

A 10 B 12 C 8 D 15 E 18 F 10 G 19;

A company manufactures products A to G using two types of machines (P1, P2) and three raw materials (R1, R2, R3). Relevant data are given below. R2 R3 Item Item input (in units) to make one unit of Max. A B C D E F G avail. per day R1 (in units) 0.10 0.30 0.20 0.10 0.20 0.10 0.20 500 0.20 0.10 0.40 0.20 0.20 0.30 0.40 750 0.20 0.10 0.10 0.20 0.10 0.20 0.30 350 Pi time (mc. hrs.) 0.02 0.03 0.01 0.04 0.01 0.02 0.04 60 P2 0.04 0.02 0.02 0.06 0.03 0.05 Req. daily > 200 200