The Bubbly Soda company produces popular soda. A special type of soda consists o

Question

The Bubbly Soda company produces popular soda. A special type of soda consists of regular and diet soda. the company has received an order for a minimum of 400000 litres of the special type. The customer specified that the blend must contain at least 40% of regular soda and not more than 250000 litres of diet soda. The customer also specified that the the blend should be mixed in the ratio of 2 parts regular to 1 part diet. The company can produce 500000 litres per week, regardless of the blend. The manager wants to complete the order in 1 week. The blend is sold for $12 per litre. The company's cost per litre is $4 for regular and $2 for diet. The company wants to determine the blend mix that will meet the customer's requirements and maximize profits.

a) Formulate algebraically a linear programming model for this problem.

Explanation / Answer

This is a case of multiple goal programmin model;
Our primary goal is to mee the customer's requirmeents;
Our next goal is to maximise the profits;
Let the blend be donated by Z
Z: (X,Y) where X is regular soda and Y is diet soda produced and sold to this customer in 1 week;

We have been given that Z = 400,000 (or more)
So X+Y >= 400,000
Cost of 1 litre X= 4
Cos of 1 litre Y = 2;
Production capacity of the company regardless of the blend = 500,000 (a week's capacity will be taken since the order is to be completed in 1 week itself)
Blend must contain at least 40% regular soda;
X>= 2/5 ( X+Y) or 3X/5 > = 2Y/5; 3X>=2Y; X/Y>=2/3
Blend must contain not more than 250,000 litres of diet soda
Y<= 250,000

Blend must be mixed in proportion of 2 parts regular to 1 part diet;
So X/Y = 2/1 = 2;
Selling price = 12$ per litre of Blend;

Profit function = selling price - csot price
= 12 ( X+Y) - 4X - 2Y = 8X + 10Y;
Objective function : Maximise 8X+10Y
Constraints:
X+Y>= 400,000 ( Customer requirement constraint)
X+Y <= 500,000 (Capacity constraint)  
X/Y > = 2/3; (40% regualr soda constraint)
X/Y=2; (Mixing parts constraint)
Y<= 250,000 (Diet soda capacity constraint)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.