Question

The Bubbly Soda (BS) Company produces popular sodas. A special type of soda consists of regular and diet soda. The company has received an order for a minimum of 400.00 litres of the special type. The customer specified that the order must contain at least 40% of regular soda and not more than 250,000 litres of diet soda. The customer also specified that the blend should be mixed in the ratio of 2 parts regular to 1 part diet. The BS Company can produce 500,000 litres per week, regardless of the blend. The production manager wants to complete the order in 1 week. The blend is sold for $12 per litre. The BS company's cost per litre is $4 and $2 for diet. The company wants to determine the blend mix that will meet customer requirements and maximize profits.

a.) Formulate algebraically a linear programming model for this problem.
b.) Solve this problem using excel (please post a screenshot when using solver)

Answer 1

Let x be the quantity of regular soda and y be the quantity of diet soda
Hence,

Cost=4x+2y
Maximize Profit=12*(x+y)-4x+2y

s.t.
x+y<=500000
2y-x<=0
x-2y<=0
-x-y<=-400000
0.4y-0.6x<=0
y<=250000

1.
x+y>=400000 or -x-y<=-400000
2.
x+y<=500000
3.
x/(x+y)>=0.4
=>0.4y-0.6x<=0
4.
x:y=2:1
=>x-2y=0
or, x-2y<=0
and x-2y>=0 or 2y-x<=0
5.
y<=250000