Problem 1.
A food company produces two types of turkey cutlets for sale to fast-food restaurants. Each type of cutlet conisists of white meat and dark meat. Cutlet 1 sells for $4 per pound and must consist of at least 70% white meat. Cutlet 2 sells for $3 per pound and must consist of at least 60% white meat. At most 6000 pounds of cutlet 1 and 2000 pounds of cutlet 2 can be sold. The two types of turkey used to manufacture the cutlets are purchased
from a turkey farm. Each type 1 turkey costs $10 and yields five pounds of white meat and two pounds of dark meat. Each type 2 turkey costs $8 and yields three pounds of white meat and three pounds of dark meat.
Determine how the company can maximize its profit.
Problem 2
Each hour from 10 a.m. to 7 p.m., a bank receives checks and must process them. Its goal is to process all checks the same day they are received. The bank has 13 check processing machines, each of which can process up to 500 checks per hour. It takes one worker to operate each machine. The bank hires both full-time and part-time workers. Full-time workers work 10 a.m. to 6 p.m., 11 a.m. to 7 p.m., or noon to 8 p.m. and are paid $160 per day. Part-time workers work either 2 p.m. to 7 p.m. or 3 p.m. to 8 p.m. and are paid $75 per day. The numbers of checks received each hour are listed in the file. In the interest of maintaining continuity, the bank believes that it must have at least three full-time workers under contract. Develop a work schedule that processes all checks by 8 p.m. and minimizes daily labor costs.
Problem 3
An oil company produces oil from two wells. Well 1 can produce up to 150,000 barrels per day, and well 2 can produce up to 200,000 barrels per day. It is possible to ship oil directly from the wells to the company’s customers in Los Angeles and New York.
Alternatively, the company could transport oil to the ports of Mobile and Galveston and then ship it by tanker to New York or Los Angeles, respectively. Los Angeles requires 160,000 barrels per day, and New York requires 140,000 barrels per day. The costs of shipping 1000 barrels between various locations are shown in the file where a blank indicates shipments that are not allowed. Determine how to minimize the transport costs in meeting the oil demands of Los Angeles and New York.
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