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Taking the standard approach to constrained optimisation, where we maximise utility subject to a budget constraint with some allocation on the consumption of two goods, does it make apply the same logic to mutually exclusive goods?

Can we also limit the consumption of either good to only 1 unit? One context of this could be applied in would be trying to find out what delivery 'subscription plan' is optimal, such as comparing between Amazon Prime and, say, a Prime equivalent to Walmart. However, there is also an element of 'quantity consumed' subject to a budget constraint after the purchase of the subscription.

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