You own a portfolio which is valued at $8.5 million and which has a beta of 1.3. You would like to create a riskless portfolio by hedging with S&P 500 futures contracts. The contract size is $250 times the index level. How many futures contracts do you need to acquire if the current S&P 500 index is 1310? Select one: a. Short 41 contracts b. Short 28 contracts c. Short 34 contracts d. Long 28 contracts e. Long 34 contracts

You are the manager of a firm that produces output in two plants. the demand for your firm's product is p = 20 − q, where q = q1 + q2. the marginal costs associated with producing in the two plants are mc1 = 2 and mc2 = 2q2. how much output should be produced in plant 1 in order to maximize profits?

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

Jack manufacturing company had beginning work in process inventory of $8,000. during the period, jack transferred $34,000 of raw materials to work in process. labor costs amounted to $41,000 and overhead amounted to $36,000. if the ending balance in work in process inventory was $12,000, what was the amount transferred to finished goods inventory?