Discuss the below:
Q: Joe R. earns extra money as a wedding photographer. He delivers prints with dimensions 4x6, 5x7 or 8x10. He uses two types of photographic paper 8x10 and 8x12 and cuts them to accommodate the 4x6 and 5x7 prints. He has 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
|
Joe has just received an order for the following numbers of prints:
136 4x6 prints
41 5x7 prints
17 8x10 prints
Q1) Assuming leftover portions of sheets have no value, find the number of sheets Joe must buy to meet this order. Compute the number of each print size that are left over.
Q2) Compute the number of square inches of wasted material for each pattern. Reformulate and solve the problem to minimize the total amount of wasted material.