Step-by-step explanation:
Let p(x) be the profit function.
[tex] \therefore \: p(x) = r(x) - c(x) \\ = 6.5x -( 0.75x + 1850) \\ = 6.5x - 0.75x - 1850 \\ \purple{ \boxed{ \bold{ \therefore \: p(x) = 5.75x - 1850}}} \\ this \: is \: the \: profit \: function. \\ \\ p(500) = 5.75 \times 500 - 1850 \\ = 2875 - 1850 \\ p(500) = 1025 \\ \\ p(1000) = 5.75 \times 1000 - 1850 \\ = 5750 - 1850 \\ p(1000) = 3900 \\ \\ p(5000) = 5.75 \times 5000 - 1850 \\ = 28750 - 1850 \\ p(5000) = 26900[/tex]
