To solve problems based upon product mix

1. P. Maria Sheeba
PG Student,
Mepco Schlenk Engineering College
PRODUCT MIX PROBLEM

2. Consider the following problem faced by a production
planner in a soft drink plant. He has 2 bottling machines A and B.
A is designed for 8 ounce bottles and B for 16 ounce botttles.
However, each can be used on both types with some loss of
efficiency. The following data is available:
Each machine can be run 8 hours per day, 5 days per week. Profit
on a 8 ounce bottle is 25 paise and on a16 ounce bottle is 35
paise. Weekly production of the drink cannot exceed 3,00,000
ounces and the market can absorb 25,000 8 ounce bottles and
7,000 16 ounce bottles per week. The planner wishes to maximize
his profit subject, of course, to all the production and marketing
restrictions.Formulate the linear programming problem to find the
product mix to maximize the profit.
PROBLEM 1
Machine 8 ounce bottles 16 ounce bottles
A 100/minute 40/minute
B 60/minute 75/minute

3. GIVEN DATA
Resource/
constraint
Production Availability
8 ounce bottle 16 ounce bottle
Machine A time 100/minute 40/minute 8x5x60
= 2400 minutes
Machine B time 60/minute 75/minute 8x5x60
= 2400 minutes
Production 1 1 3,00,000 ounces
per week
Marketing 1 - 25,000 units per
week
Marketing - 1 7,000 units per
week
Profit/unit (Rs.) .25 .35

4. 1. Key decision: Determine the no of bottles to be produced per week (8
ounce and 16 ounce).
2. Identification of Variables: The weekly production of 8 ounce and 16
ounce bottles.
Designation of variables:
 Weekly production of 8 ounce bottles = x1 bottles.
 Weekly production of 16 ounce bottles = x2 bottles.
3. Feasible alternatives: x1 ≥ 0, x2 ≥ 0.
4. Constraint:
1. Machine time
 x1/100+ x2/40 ≤ 2400. (Machine A)
 x1/60 + x2/75 ≤ 2400. (Machine B)
2. Production constraints
 8x1 + 16x2 ≤ 3,00,000.
3. Market constraints
 x1 ≤ 25,000
 x2 ≤ 7,000
5. Objective: To maximize the total profit from sales
 z = 0.25x1 + 0.35x2.
SOLUTION

5. Find x1, x2 so as to maximize
z = 0.25x1 + 0.35x2.
Subject to the constraints:
 x1/100+ x2/40 ≤ 2400.
 x1/60 + x2/75 ≤ 2400.
 8x1 + 16x2 ≤ 3,00,000.
 x1 ≤ 25,000
 x2 ≤ 7,000
 x1 ≥ 0, x2 ≥ 0.
MATHEMATICAL FORMAT

6. THANK YOU