Reflections

1

• Lab 3-8
• In designing your recycling business for
  efficiency, you need to know how best to allocate
  your equipment budget. A part of this process is
  determining how many of each major piece of
  equipment should be purchased.
• For this project you need to decide how many
  glass recycling machines and plastic recycling
  machines to buy. You need to consider each
  machine type's capacity, floor space
  requirements, and cost, as given in the following
  table
• Translate the following constraints into a system
  of linear inequalities. Let G represent the
  number of glass recycling machines (x for our
  calculator) and P the number of plastic recycling
  machines (y for our calculator).a. C1 The
  facility needs to be able to process at least 10
  tons of glass per hour. b. C2 The
  facility needs to be able to process at least 7
  tons of plastic per hour. c. C3 The
  total floor space available for the machines is
  3400 square feet d. C4 The budget for
  recycling machines is 300,000
• Your objective is to maximize the total value of
  recycled material that can be processed in one
  hour. Assuming recycled glass has a value of
  112 per ton and recycled plastic has a value of
  235 per ton, write an equation for the value of
  recycled material that is produced in one hour by
  G glass recycling machines and P plastic
  recycling machines (assuming that all machines
  work at full capacity)V

Recycling Machine Glass Plastic
Capacity 3.2 tons/hour 1.6 tons/hour
Floor Space 180 sq. ft. 205 sq. ft.
Cost 14,500.00 19,600.00

2

1. Use the following table to list the four corner
   points and determine the maximum value of the
   recycled material based upon the corner points.
2. Is the solution you determined in Problem 3
   really feasible? Yes or No Why?
3. If you simply rounded the values for G and P in
   table in 3, would you have a feasible solution?
   Yes or No Check by substituting into
   each constraint inequality. a. C1b.
   C2c. C3d. C4
4. Since the number of machines of either type must
   be whole numbers (positive integers), when the
   coordinates of the corner points include decimal
   fractions they are actually not feasible, as is
   the case in this problem. These are called
   integer linear programming problems a special
   class of problems requiring different solution
   techniques. Consider the five integer solutions
   that are in the feasible region closest to the
   max corner point. Determine the objective
   function at each solution.Note (11,7) is not
   in feasibleregion

G P V G P




G P V G P

1. What is the maximum value of recyclables that can
   be processed in one hour?
2. How does this compare to the value you got in
   table 3 above?

7 6 5
11 12 13 14