3. A young girl is opening a lemonade stand in front of her house. It cost her $12 to buy lemonade mix and uses all of it. She buys a pack of 300 cups for
$5. She also buys a pitcher for $4. Each pitcher holds 8 cups of lemonade.
She sells 106 cups of lemonade that day. She charges 50 cents a cup for the
lemonade.

Sailors went to special school to learn how to use the new technology that would them sail far distences. the school we know about was

What is the rule relating the ratio of marginal utility to prices of two goods at the optimal choice? explain why, if this rule does not hold, the choice cannot be utility-maximizing.

It is widely assumed that people need to engage in intellectual activities such as solving crossword puzzles or mathematics problems in order to maintain mental sharpness as they age. in fact, however, simply talking to other people—that is, participating in social interaction, which engages many mental and perceptual skills—suffices. evidence to this effect comes from a study showing that the more social contact people report, the better their mental skills. which of the following, if true, most seriously weakens the force of the evidence cited? (a) as people grow older, they are often advised to keep exercising their physical and mental capacities in order to maintain or improve them. (b) many medical conditions and treatments that adversely affect a person's mental sharpness also tend to increase that person's social isolation. (c) many people are proficient both in social interactions and in solving mathematical problems. (d) the study did not itself collect data but analyzed data bearing on the issue from prior studies. (e) the tasks evaluating mental sharpness for which data were compiled by the study were more akin to mathematics problems than to conversation.