please help

Problem 1 Applying the one input] one output model (Lecture Recording and Handout 03/26) Mr. X is a selfsemployed limousine driver. Each day, if driving L hours Mr. X can complete q = 104E rides. Mr. X charges P = $9 for each drive. If he didn't drive a Taxi, Mr. X could nd a minimum wage job and earn $15 an hour (this is the implicit cost of dn'ving the tax an extra hour). Currently, Mr. X rents the limousine from a neighbor for one third of his daily revenue (hence Rent = 1/ 3 x 39 x 104:). a) Wdte Mr. X's revenue from his daily rides as a inction of the number of hours he drives. b) Write Mr. X's eost (include the implicit cost of labor and the explicit cost from renting the Limo) c) Write Mr. X's prot function1 that is prot as a function of the variable input L. d) Find M. X's optimal (prot maximizing) number of hours spent driving. e) In a diagram, measuring driven hours along the horizontal axis draw Mr. X's short run production function. f) In the same diagram, add isoprot lines to illustrate Mr. X's prot maximizing number of hours driven. g) Now, using the information above, compute the rent Mr. X pays to his neighbor for the use of the Limo. One day, the neighbor suggests a change in the stmcture of the rental agreement and asks Mr. X to pay him a at rent of $70 per day instead. h) How does the change in the rental agreement affect Mr. X's prot function? i) How does the change the rental agreement affect the number of hours Mr. X spends diiving? j) Does the change in the rental agreement make Mr. X better off or worse off