Ecan read from these graphs that the absolute minimum is about 0 incorrect: your answer is incorrect. and occurs when x ≈ 1.5 incorrect: your answer is incorrect. in the second graph. there is also a local maximum ≈ 0.00002 when x ≈ in the third graph and a local minimum ≈ 211 when x ≈ in the last graph. these graphs also show three inflection points near −35, −5, and −1 and two between −1 and 0. to estimate the inflection points closely we would need to graph f '', but to compute f '' by hand is an unreasonable chore. if you have a computer algebra system, then it's easy to do. (see this exercise.)

1. an economy consists of three workers: larry, moe, and curly. each works 10 hours a day and can produce two services: mowing lawns and washing cars. in an hour, larry can either mow one lawn or wash one car; moe can either mow one lawn or wash two cars; and curly can either mow two lawns or wash one car. a. calculate how much of each service is produced under the following circumstances: a. all three spend all their time mowing lawns. b. all three spend all their time washing cars. c. all three spend half their time on each activity d. larry spends half of his time on each activity, while moe only washes cars and curly only mows lawns b. using your answers to part a, draw a production possibilities frontier and label points a, b, c, and d on your graph. explain why the production possibilities frontier has the shape it does. c. are any of the allocations calculated in part a inefficient? explain.