Person 1 cares about both her income and person 2's income. Precisely, the value she attaches to each unit of her own income is the same as the value she attaches to any two units of person 2's income. For example, she is indifferent between a situation in which her income is 1 and person 2's is 0, and one in which her income is 0 and person 2's is 2. How do her preferences order the outcomes (1, 4), (2, 1), and (3, 0), where the first component in each case is her income and the second component is person 2's income? Give a payoff function consistent with these preferences.

Laval produces lamps and home lighting fixtures. its most popular product is a brushed aluminum desk lamp. this lamp is made from components shaped in the fabricating department and assembled in the assembly department. information related to the 22,000 desk lamps produced annually follows.direct materials $280,000direct labor fabricating department (8,000 dlh × $24 per dlh) $192,000assembly department (16,600 dlh × $26 per dlh) $431,600machine hours fabricating department $15,200mhassembly department $20,850mhexpected overhead cost and related data for the two production departments follow.fabricating assemblydirect labor hours 150,000dlh 295,000dlhmachine hours 161,000mh 128,000mhoverhead cost $400,000 430,000required1. determine the plantwide overhead rate for laval using direct labor hours as a base.2. determine the total manufacturing cost per unit for the aluminum desk lamp using the plantwide overhead rate.3. compute departmental overhead rates based on machine hours in the fabricating department and direct labor hours in the assembly department.4. use departmental overhead rates from requirement 3 to determine the total manufacturing cost per unit for the aluminum desk lamps.