Explain why utility maximization subject to the budget constraint implies that the consumer purchases that basket of commodities for which a. all...

Explain why utility maximization subject to the budget constraint implies that the consumer purchases that basket of commodities for which

a. all income is used up.

b. the marginal rate of substitution equals the price ratio.

c. the marginal utilities per dollar of the two goods are equal. 

Please draw a diagram to explain