Answer to Question #114341 in Operations Research for sana

Question

a company manufactures two kinds of ice cream. the vanilla ice-cream sells for $2.50 each while the chocolate flavor ice-cream sells for $4.50 cents each. it costs the company 1 labor hour to make the vanilla flavor ice-cream and 2 labor hours to make the chocolate flavor ice-cream. the company has a total of 300 labor 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 400 machine hours available. how much of each type of ice-cream should the company produce to maximize the revenue? what is the maximum revenue? [ Hint: let vanilla ice-cream = x ]

Answer 1

vanilla ice-cream = x

chocolate ice-cream = y

x*1 + y*2 <= 300

x*3 + y*2 <= 480

find x and y, when 2.50*x+4.50*y-max

lets Z- max value

so we have:

x + 2y = 300

3x + 2y = 480

2.5x+4.5y=Z

we can multiply the first equation by -1 and lets add two equations

2x=180, so x=90

y=(300-x)/2 = 105

Z = 2.5*90+4.5*105 = 697.5

x = 90 - vanilla ice-cream

y = 105 - chocolate ice-cream

max = 697.5