Georges, the owner of Maison d'Ail, earned his coveted Michelin star rating by smothering his dishes in freshly minced garlic. Georges knows that he can save labor costs by using less garlic, albeit with a reduction in quality. If Georges puts g garlic cloves in a dish, the dish's quality, z, is z = 1/2g0.5. Georges always fills his restaurant to its capacity, 250 seats. He knows that he can raise the price of each dish by 40¢ for each unit increase in quality and continue to fill his restaurant. Jacqueline, who earns $10 per hour, minces Georges' garlic at a rate of 120 garlic cloves per hour.
a. What is Jacqueline's value of marginal revenue product?
b. How many hours per afternoon (while the kitchen prep work is being done) does Jacqueline work?
c. How many minced cloves of fresh garlic does Georges put in each dish?