Suppose that a government auctions 40 licenses each month. last month, in the first auction, 25 people bid 3.2 pounds of protein, 20 people bid 3.1 pounds, 15 people bid 3.0 pounds, 5 people bid 2.9 pounds, and 10 people bid 2.8 pounds.

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

As sales exceed the break‑even point, a high contribution‑margin percentage (a) increases profits faster than does a low contribution-margin percentage (b) increases profits at the same rate as a low contribution-margin percentage (c) decreases profits at the same rate as a low contribution-margin percentage (d) increases profits slower than does a low contribution-margin percentage

Miller mfg. is analyzing a proposed project. the company expects to sell 14,300 units, plus or minus 3 percent. the expected variable cost per unit is $15 and the expected fixed cost is $35,000. the fixed and variable cost estimates are considered accurate within a plus or minus 3 percent range. the depreciation expense is $32,000. the tax rate is 34 percent. the sale price is estimated at $19 a unit, give or take 3 percent. what is the net income under the worst case scenario?