Answer to Question #113908 in Operations Research for Praneeta singh

Question #113908
A company manufactures two kinds of ice-cream. The vanilla ice-cream sells for $2.50 each while
the chocolate flavour ice-cream sells for $4.50 cents each. It costs the company 1 labour hour to
make the vanilla flavour ice-cream and 2 labour hours to make the chocolate flavour ice-cream.
The company has a total of 300 labour hours available. It costs the company 3 machine hours for
the vanilla ice-cream and 2 machine hours for the chocolate ice-cream. The company has a total
of 480 machine hours available. How much of each type of ice-cream should the company
produce to maximise revenue? What is the maximum revenue? [Hint: let vanilla ice-cream = x]
1
Expert's answer
2020-05-05T20:14:35-0400

x - quantity vanilla ice-cream;

y - quantity chocolate ice-cream.

"2.50x+4.50y \\to max;"

"1x+2y=300"

"3x+2y=480;"

"x=300-2y;"

"3\u00d7(300-2y)+2y=480;"

"900-6y+2y=480;"

"420=4y;"

"y=105;"

"x=300-2\u00d7105=90;"

"2.50\u00d790+4.50\u00d7105=225+472.5=\\$ 697.5;"

Answer: $ 697.5 - maximum revenue, 90 a portion vanilla ice-cream, 105 a portion chocolate ice-cream.


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