Answer to Question #113770 in Algebra for Archana

Question

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]

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 build the grafic

green- y=150-0.5x

blue- y=240-1.5x

selected field is the area where the solution will be

we can build where 2.50*x+4.50*y will be some value

for examaple:

2.50*x+4.50*y=1.5 ( y = 3/7-(5/7)x )

2.50*x+4.50*y = 100 ( y = 200/7-(5/7)x )

also, note, that x and y more then zero(count can be less)

as we can see, we need value, less then in first grafic, but maximum value, so it will be at the intersection of two graphs

when: y=150-0.5x=240-1.5x

x = 90 - vanilla ice-cream

y = 105 - chocolate ice-cream

so, 2.50*x+4.50*y with that value:

max = 1395/2