Question 91) Friendly Manufacturing has three factories (1, 2, and 3)

91) Friendly Manufacturing has three factories (1, 2, and 3) and three warehouses (A, B, and C). The table below shows the shipping costs between each factory (in dollars) and warehouse, the factory manufacturing capabilities (in 1000s), and the warehouse capacities (in 1000s). Write the objective function and the constraint inequalities. Let X1A = 1000s of units shipped from factory 1 to warehouse A, etc.

92) The following table provides shipping costs from each of two regional warehouses to each of three destinations. The supplies available and the demands are also given in the table.

Formulate this as a linear programming problem. Carefully define all decision variables.

93) Green Grass, Inc. just ran out of stock and suddenly has two emergency orders for grass seed blends: one is for 1500 pounds of normal, the other for 2300 pounds of special. At least each pound of normal should contain 60 percent annual seed, while each pound of special should contain at least 70 percent perennial seed. Green Grass has two input mixtures, A and B. Mixture A contains 80 percent perennial and 15 percent annual seed. Mixture B contains 70 percent annual and 25 percent perennial seed. Mixture A costs 90 cents per pound and mixture B costs 50 cents per pound. Set up the constraints and the objective function to solve this blending problem.

94) Three types of gasoline are manufactured by a company – Regular, Super, and Extra. Regular should have at least 11 percent additive 1 and 17 percent additive 2. Super should have at least 13 percent additive 1 and 22 percent additive 2. Extra should have at least 17 percent additive 1 and 19 percent additive 2. These are made by using two crudes – A and B. Crude A cost $28 per barrel and is 14 percent additive 1 and 18 percent additive 2. Crude B costs $30 per barrel and is 20 percent additive 1 and 24 percent additive 2. The demand for Regular is projected to be 1,000 barrels, while each of the others has a demand of 2,000 barrels. Formulate this as a linear programming problem to minimize cost while meeting all constraints. Carefully define all decision variables.

95) Three types of fertilizer are manufactured by a company: Regular, Supergro, and Jungle Feeder. Regular should have at least 10 percent nitrogen and 16 percent phosphorous. Supergro should have at least 12 percent nitrogen and 20 percent phosphorous, and Jungle Feeder should have at least 15 percent nitrogen and 18 percent phosphorous. These are made by using two components: A and B. Component A costs $0.30 per pound and is 14 percent nitrogen and 18 percent phosphorous. Component B costs $0.50 per pound and is 20 percent nitrogen and 24 percent phosphorous. The demand for Regular is projected to be 1,000 pounds, while each of the others has a demand of 2,000 pounds. Formulate the appropriate linear program.

96) A cruise line is planning its menu for the next trip. Vacationers like eating steak, lobster, and chicken. The cruise line has decided to plan for at least half of all booked passengers to have a steak dinner, for at least a quarter of all passengers to have lobster, and the rest to have chicken. Steak dinners cost the company $8, lobsters cost $15, and chicken costs the line $4. On the next cruise, there are 400 passengers booked. In addition, the cruise line has decided to plan for an additional 25% more meals than bookings. Formulate the appropriate linear program.

97) A mail order firm, AmazingCo, can use one of 3 shipping couriers. Ajax Shipping charges $6 per pound and delivers in 2 days. Bilco Lanes charges $9 per pound but guarantees next day delivery. The final courier, Hobo Ltd., charges only $3 per pound but takes 4 days to deliver. AmazingCo has a quarterly budget of $280,000 and a reputation for timely delivery. Formulate the linear program so that the firm delivers as fast as possible within budget for 70,000 pounds of shipments per quarter.

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