There are two types of mba students, movers and shakers. both types of students are valuable to potential employers but movers are more valuable. employers would be willing to pay a mover a $150,000 salary, but only $100,000 for a shaker. unfortunately, it is difficult to tell the difference between the two. one key difference between the two types of students is in the pain that economics courses cause them. for movers, an economics course causes about $6,000 in pain, at least that is how much salary they would be willing to give up to avoid an economics course. the shakers value the pain at $9,000 per course. a recruiting firm wants to devise a self-selection mechanism to separate the movers and the shakers. once the two types are identified, they will be paid $150,000 and $100,000 respectively. what is the minimum number of economics courses that a firm can require a student to take in order to receive the mover salary? what is the maximum number of courses? b. who bears the cost of signaling their quality?

Needs to schedule the staffing of the center. it is open from 8am until midnight. larry has monitored the usage of the center at various times of the day and determined that the following number of computer consultants are required: time of dayminimum number of consultants required to be on duty8 am-noon4noon-4 pm84pm-8pm108pm-midnight6 two types of computer consultants can be hired: full-time and part-time. the full- time consultants work for eight consecutive hours in any of the shifts: morning (8am- 4pm), afternoon (noon-8pm) and evening (4pm-midnight). full-time consultants are paid $14 per hour. part-time consultants can be hired to work any of the four shifts listed in the table. part-time consultants are paid $12 per hour. an additional requirement is that during every time period, there must be at least two full-time consultants on duty for every part-time consultant on duty. larry would like to determine how many full-time and part-time consultants should work each shift to meet the above requirements at the minimum possible cost. formulate this as an lp problem. you must define your variables clearly

1. what is the lowest balance during this period? 2. lily just received her bank statement below. a. what does the bank think her ending balance is? b. how much more does the bank think lily has? c. what transactions are missing? 3. what is the danger of not balancing your bank account? lily’s bank statement deposits: 2/25 $35 2/26 $20 3/1 $256.32 checks: 2/24 ck #301 $25 2/26 #302 $150 debit card: 2/24 american eagle $75.48 2/25 chick fa la $4.67 2/27 mcdonalds $3.56 2/28 chevron $34.76 withdrawal: 2/27 $40 beginning balance $423.34 deposits $311.32 total debits $333.47 ending balance $401.19

David consumes two things: gasoline (g) and bread (b). david's utility function is u(g, b) = 10g^0.25 b^0.75. use the lagrange technique to solve for david's optimal choices of gasoline and bread as a function of the price of gasoline, p_g, the price of bread, p_b, and his income m. with recent decrease in the price of gasoline (maybe due to external shock such as shale gas production) does david increase his consumption of gasoline? for david, how does partial differential g/partial differential p_g depend on his income m? that is, how does david's change in gasoline consumption due to an increase in the price of gasoline depend on his income level? to answer these questions, find the cross-partial derivative, |partial differential^2 g/partial differential m partial differential p_g.