9.3 Sam Malone is considering renovating the bar stools at Cheers. The production function for new bar stools is given by 9=0.10.210.8 where q is the number of bar stools produced during the renovation week, k represents the number of hours of bar stool lathes used during the week, and I represents the number of worker hours employed during the period. Sam would like to provide 10 new bar stools, and he has allocated a budget of $10,000 for the project.

a. Sam reasons that because bar stool lathes and skilled bar stool workers both cost the same amount ($50 per hour), he might as well hire these two inputs in equal amounts. If Sam proceeds in this way, how much of each input will he hire and how much will the renovation project cost?

b. Norm (who knows something about bar stools) argues that once again Sam has forgotten his microeconomics. He asserts that Sam should choose quantities of inputs so that their marginal (not average) productivities are equal. If Sam opts for this plan instead, how much of each input will he hire and how much will the renovation project cost?

c. Upon hearing that Norm's plan will save money, Cliff argues that Sam should put the savings into more bar stools in order to provide seating to more of his USPS colleagues. How many more bar stools can Sam get for his budget if he follows Cliff's plan?

d. Carla worries that Cliff's suggestion will just mean more work for her in delivering food to bar patrons. How might she convince Sam to stick to his original 10-bar stool plan?