Can someone help me out here, thanks!Incorrect/Nonsense = delete

Minimum [tex]\bold{C = 56}[/tex] at [tex]\bold{(x, y) = (7, 3)}[/tex].Here's Why:Given:Minimize [tex]C = 5x + 7y[/tex] subject to:     [tex]x + y = 10[/tex]     [tex]x \geq 2[/tex]     [tex]y \geq 3[/tex]From [tex]x + y = 10[/tex], express [tex]y = 10 - x[/tex].Substitute into [tex]C[/tex]:      [tex]C = 5x + 7(10 - x) = 5x + 70 - 7x = 70 - 2x[/tex]To minimize [tex]C[/tex], maximize [tex]x[/tex]  because of the [tex]-2x[/tex] term.Constraints on [tex]x[/tex] are:     [tex]x \geq 2, \quad y = 10 - x \geq 3 \implies 10 - x \geq 3 \implies x \leq 7[/tex]So [tex]x \in[/tex].Maximize [tex]= 7[/tex]:      [tex]C = 70 - 2(7) = 70 - 14 = 56[/tex]At [tex]x = 7[/tex], [tex]y = 3[/tex].

Answered by Sefton | 2025-08-11