U($1, .122) = sci/5.12:\" Q4: Calculate the marginal utility of meat. Briey explain what happens to the marginal utility of meat as the agent consumes more potatoes. Q5: Calculate the marginal rate of substitution of potatoes for meat. Briey explain how the marginal rate of substitution depends on the relative quantities of meat and potatoes the agent consumes. Qa: Write down the two mathematical conditions that the consumer's optimal bundle must satisfy. Briey explain how you would interpret each condition in economic terms (income, utility per dollar, etc). Qb: Derive the optimal consumption bundle for the consumer using the budget and preferences described above. Show your work. Label this point on the same graph you drew in Q2 and draw the indifference curve that corresponds to the optimal bundle. Consider again the original budget constraint and utility function. Now, suppose the price of meat inereasa from $5 to $10 per pound. Q7: Derive the new optimal consumption point. Draw and label the new budget line and optimal consumption point on the same graph from Q2. Draw and label the indierence curve corresponding to the new optimal bundle