The current exchange rate of dollars to euros is $18/€11.The risk free rate for dollars is r = 3%. The risk free rate for euros is re = 4%. The dollar denominated price of an option to purchase €22 for $32 in six months is $5.09. Determine the euro denominated price of a put option to sell $22 in six months using the given strike. (Hint: the strike comes from the statement €22 for $32.)

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

Jamie lee is reviewing her finances one month later. she has provided the actual amounts paid below. use the cash budget table below to her identify the variances in her budget. each answer must have a value for the assignment to be complete. enter "0" for any unused categories. actual amounts income: monthly expenses: gross monthly salary $2,315 rent obligation $260 net monthly salary $1,740 utilities/electricity $130 savings allocation: utilities/water $10 regular savings $130 utilities/cable tv $155 rainy-day savings $20 food $160 entertainment: gas/maintenance $205 cake decorating class $90 credit card payment $25 movies with friends $50 car insurance $75 clothing $145 budgeted amounts assets: monthly expenses: checking account $1,850 rent obligation $225 emergency fund savings account $4,300 utilities/electricity $75 car $5,200 utilities/water $35 computer & ipad $1,100 utilities/cable tv $120 liabilities: food $115 student loan $6,600 gas/maintenance $95 credit card balance $1,000 credit card payment $45 income: car insurance $45 gross monthly salary $2,155 clothing $45 net monthly salary $1,580 entertainment: savings allocation: cake decorating class $90 regular savings $130 movies with friends $50 rainy day savings $20

Zapper has beginning equity of $257,000, net income of $51,000, dividends of $40,000 and investments by stockholders of $6,000. its ending equity is