Sam Peters keeps a secondary job as a photographer Sam makes

Sam Peters keeps a secondary job as a photographer. Sam makes photo prints with dimensions 4x6, 5x7 or 8x10. Using two types of photographic paper 8x10 and 8x12 and cuts them to accommodate the 4x6 and 5x7 prints. Sam has aslo identified the patterns in the table below using the notation Xij where i=1 for patterns cut from an 8x10 sheet and i=2 for patterns cut from 8x12 sheets. 8x10 sheets cost $1 and 8x12 sheets cost $1.25.

Pattern

4x6

5x7

8x10

X10

0

0

1

X11

0

1

0

X12

0

2

0

X13

1

0

0

X14

2

0

0

X15

3

0

0

X16

1

1

0

X20

0

0

1

X21

0

1

0

X22

0

2

0

X23

1

0

0

X24

2

0

0

X25

3

0

0

X26

4

0

0

X27

1

1

0

X28

2

1

0

Sam recently received an order for the following numbers of prints:

136 4x6 prints

41 5x7 prints

17 8x10 prints

Start by formulating a  LINDO script, constraints and variables.

1) With the assumption that leftover portions of sheets have no value find the number of sheets of each size that Sam must buy to meet this order at minimum cost. Determine the number cut of each beyond the number ordered.

2) Determine the number of square inches of wasted material for each pattern.Reformulate and solve the problem to minimize the total amount of waste. Determine the excess number cut of each size for this solution.

Pattern	4x6	5x7	8x10
X10	0	0	1
X11	0	1	0
X12	0	2	0
X13	1	0	0
X14	2	0	0
X15	3	0	0
X16	1	1	0
X20	0	0	1
X21	0	1	0
X22	0	2	0
X23	1	0	0
X24	2	0	0
X25	3	0	0
X26	4	0	0
X27	1	1	0
X28	2	1	0

Solution

Variable        Value                 Reduced Cost

4*6         $1.00000000             0.00

5*7         $1.25000000             0.00

SETS:

Photo8x10 and 8x12 Capacity;ENDSETS

@FOR(Photos(P): Capacity(T)<4x6>

@FOR(Photos(P): Capacity(T)<5x7>

@FOR(Photos(P): Capacity(T)<8x10>

SETS:

Photo/X Y/;

Reduced cost/L M/;

Make (Photo reduced cost) / X L, X M, Y M/;

ENDSETS

SETS

X L, X M, Y M

136 ORDERS =68SHEETS NEEDED,$68

41 ORDERS=11SHEETS NEEDED,$13.75

____________________________________________________________________

2)

SETS:

4x6, 5x7 or 8x10. Using two types of photographic paper

SETS:

square inches

(136 4x6) =(46.65)2

(41 5x7 )=(24.80)2

SETS:

Total Waste

2,176 + 615=2,791

SETS:

Excess

(136 4x6)8x10 =2,176

(41 5x7 )8x12 =615

(17 8x10 )8*10=NIL