Acompany is currently producing a carpet shampooer that sells about 4,000 units per year. it takes 2 hours to produce the unit, but 8 hours to set up the line for that process. this device is produced in batches of 100. management is considering producing a second type of shampooer, for which it estimates that demand would 2,000 units per year, processing time would be 2.8 hours per unit, with a setup time of 16 hours per batch, and batches of 200. there are currently two machines dedicated to the first product, which could also be used by the new one. the plant works two eight-hour shifts per day for 250 days per year, and frowns on overtime. because of uncertainties in the introduction of the new product, the company would like to reserve a capacity cushion of 10%. if management decides to go with the new product, how do you recommend that they expand to meet expected demand?

3. saving two consumers, larry and jeff, have utility functions defined over the two periods of their lives: middle age (period zero) and retirement (period 1). they have the same income in period 0 of m dollars and they will not earn income in period 1. the interest rate they face is r. larry’s and jeff’s utility functions are as follow. = 0.5 + 0.5 and = 0.5 + 0.5 for each person is between zero and one and represents each consumer’s temporal discount econ 340: intermediate microeconomics. ben van kammen: purdue university. rate. a. write the budget constraint that applies to both jeff and larry in terms of consumption in each period and ), interest rate, and m. b. what is larry’s and what is jeff’s marginal rate of intertemporal substitution? c. what is the slope of the budget constraint? d. write each consumer’s condition for lifetime utility maximization. e. re-arrange the conditions from part (d) to solve for the ratio, . f. if > which consumer will save more of his middle age income? g. if > 1 1+ , in which period will larry consume more: = 0 or = 1?