A political candidate is planning his media budget for an upcoming election. he has $90,500 to spend. His political consultants have provided him with the following estimates of additional votes as a result of the advertising effort: For every small sigh placed by the roadside, he will garner 10 additional votes For every large sign placed by the roadside, he will garner 30 additional votes For every thousand bumper stickers placed on cars, he will garner 10 additional votes For every hundred personal mailings to registered voters, he will garner 40 additional votes, For ever radio ad heard daily in the last month before the election, he will garner 485 additional votes
Advertising Medium Cost minimum Maximum Bumper stickers (thousands) $30.00 40 100 Personal mailings (hundreds) $81.00 500 800 Radio ads (per day) $1,000.00 3 12 Small road side signs $25.00 100 500 Large road side signs $60.00 50 300
The load master for a freighter wants to determine the mix of cargo to be carried on the next trip.The ship’s volume limit for cargo is 100,000 cubic meters , and its weight capacity is 2,310 tons.The master has five different types of cargo from which to select and wishes to maximize the value of the selected shipment. However, to make sure that none of his customers are ignored, the load master would like to make sure that at least 20% of each cargo’s available weight is selected. The specifications for the five cargoes are shown in the following table
cargo type Tons Available Value Per Ton Volume Per TONE A 970 $1,350.00 26 B 850 $1,675.00 54 C 1900 $1,145.00 28 D 2300 $850.00 45 E 3600 $1,340.00 37
A nursing home employs attendants who are needed around the clock. Each attendant is paid the same, regardless of when his or her shift begins. Each shift is 8 consecutive hours. Shifts begin at 6 A.M., 10 A.M., 2 P.M., 6 P.M., 10 P.M., and 2 A.M. The following table shows the nursing home’s requirements for the numbers of attendants to be on duty during specific time periods
SHIFT TIME NUMBER OF ATTENDANTS A 2-6 A.M. 8 B 6-10 A.M. 27 C 10 A.M – 2 P.M. 12 D 2-6 P.M. 23 E 6-10 P.M. 29 F 10 P.M. – 2 A.M. 23
(a) What is the minimum number of attendants needed to satisfy the nursing home’s requirements? (b) the nursing home would like to use the same number of attendants determined in part (a) but would like to minimize the total salary paid. Attendants are paid $16 per hour during 8 A.M.- 8 P.M.,and a 25% premium per hour during 8 P.M. – 8 A.M. How should the attendants now be scheduled?
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