Assume a consumer has maximized her utility by buying two products: cupcakes and cheese. her marginal utility for the last cupcake is 30. if the price of cupcakes is $3 and the price of cheese is $5, how much is her marginal utility for her last unit of cheese?

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

There is a small, family-owned store that sells food and household goods in a small town. the owners have good relations with the community, especially with local farmers who supply much of the food. the farmers aren't organized into a cooperative or union, and the store deals with each individually. suppose the store wanted to buy some farms to control the supply of certain vegetables. how would you classify this strategic move? select one: a. horizontal integration b. forward integration c. backward integration d. concentric integration

According to management education expert ashok rao, companies can increase their profitability by through careful inventory management. a. 5% to 10% b. 10% to 25% c. 20% to 50% d. 75%