In order to maximize the profit [tex]50[/tex] pints of chocolate concussion should produce.
" Linear programming is defined as it represents the extreme value of the given linear function with given subject to constraints."
According to the question,
[tex]'x'[/tex] represents the number of chocolate concussion
[tex]'y'[/tex] represents the number of Vanilla Brain Freeze
[tex]'z'[/tex] represents the maximize cost
As per the given condition of linear programming,
Maximize Cost [tex]z =5x + 7y[/tex]
Subject to constraint
[tex]6x + 9y \leq 360\\\\8x + 5y \leq 400\\\\x\geq 0, y\geq 0[/tex]
For
[tex]6x + 9y \leq 360[/tex]
[tex]x= 0 \implies y=40\\\\y=0 \implies x=60[/tex]
And
For
[tex]8x + 5y \leq 400\\\\x=0 \implies y=80\\\\y=0 \implies x= 50[/tex]
Cost for each value of given linear programming we have,
[tex](x, y) = (0,40) \\\\\implies z = 5(0) + 7(40)\\\\ \implies z = $280[/tex]
[tex](x, y) = (60,0) \\\\\implies z = 5(60) + 7(0)\\\\ \implies z = $300[/tex]
[tex](x, y) = (0,80) \\\\\implies z = 5(0) + 7(80)\\\\ \implies z = $560[/tex]
[tex](x, y) = (50,0) \\\\\implies z = 5(50) + 7(0)\\\\ \implies z = $250[/tex]
To maximize the profit [tex]50[/tex] pints of chocolate concussion.
Hence, Option (C) is the correct answer.
Learn more about linear programming here
https://brainly.com/question/15762941
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