Let model $1$ be the current model, and let model $2$ be the model where both resource availabilities have been increased by $25\%.$ Which of the following is true about the optimal solutions to these two models?

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a$.$ The optimal production quantities for exactly $4$ of the $5$ products are the same for the two optimal solutions.

b$.$ The optimal total profit for model $2$ is more than $10\%$ larger than the optimal total profit for model $1.$

c$.$ At least one of the resource constraints in model $2$ is binding.

d$.$ None of these choices are true.