The FarmerFarmer Restaurant Group manufactures the bags of frozen French fries used at its franchised restaurants. Last week, Farmer'sFarmer's purchased and used 101 comma 000101,000 pounds of potatoes at a price of $ 0.70$0.70 per pound. During the week, 2 comma 2002,200 direct labor hours were incurred in the plant at a rate of $ 12.50$12.50 per hour. The standard price per pound of potatoes is $ 0.85$0.85, and the standard direct labor rate is $ 12.30$12.30 per hour. Standards indicate that for the number of bags of frozen fries produced, the factory should have used 99 comma 00099,000 pounds of potatoes and 2 comma 0002,000 hours of direct labor. Read the requirementsLOADING Requirement 1. Determine the direct material price and quantity variances. Be sure to label each variance as favorable or unfavorable. (Enter the variances as positive numbers. Enter currency amounts to the nearest cent and your answers to the nearest whole dollar. Label the variances as favorable (F) or unfavorable (U). Abbreviations used: DM = Direct materials.)

How supply and demand work together to reach the equilibrium price in the marketplace? give at least a paragraph. you!

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

Alarge tank is filled to capacity with 500 gallons of pure water. brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gal/min. the well-mixed solution is pumped out at the same rate. find the number a(t) of pounds of salt in the tank at time t.