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Let [itex]\alpha[/itex]>0 and [itex]\gamma[/itex]>0 and [itex]\beta[/itex]>0 be real numbers. Let M={x∈R[itex]^{2}_{+}[/itex] ∶[itex]\alpha[/itex]x[itex]_{1}[/itex]+[itex]\gamma[/itex]x[itex]_{2}[/itex][itex]\leq[/itex][itex]\beta[/itex]}. Prove M is a convex set. Prove that M is bounded. What does this set resemble (in economics)?

I have a little idea of how to show that this set is convex, although, I know the condition for a convex set (ax1+(1-a)x2, 0<a<1). It is clear to me that this set resembles PPF, so can you just show me how to prove that it is convex, please.

I have a little idea of how to show that this set is convex, although, I know the condition for a convex set (ax1+(1-a)x2, 0<a<1). It is clear to me that this set resembles PPF, so can you just show me how to prove that it is convex, please.

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