Topic: Linear Programming A farmer has 10 acres to plant in wheat and rye. He has _t9_ plant at least 7 acres. However, he has only $1200 to Spend and each acre of wheat costs $200 to plant and each acre of rye costs $100 to plant. Moreover, the farmer l_1_a_s _tp_ get the planting done in 12 hours and it takes an hour to plant an acre of Wheat and 2 hours to plant an acre of rye. The prot is $500 per acre of wheat and $300 per acre of rye. The goal of the farm is to maximize the total prot. Formulate the problem with objective rnction and constraints A stereo mail order center has 8,000 cubic feet available for storage of its private label loudSpeakers. The ZAR3 speakers cost $295 each and require 4 cubic feet of space; the ZAR-2ax Speakers cost $110 each and require 3 cubic feet of space; and the ZAR4 model costs $58 and requires 1 cubic foot of space. The demand for the ZAR-3 is at most 20 units per month. The wholesaler has $100,000 to Spend on loudspeakers this month. Each ZAR3 contributes $105, each ZAR2ax contributes $50, and each ZAR4 contributes $28. The objective is to maximize total contribution. Write out the objective and the constraints. A publisher has orders for 500 copies of a certain textbook from San Francisco and 600 copies from Sacramento. The publisher has 700 copies in a warehouse in Novato and 400 copies in a warehouse in Lodi. It costs $5 to ship a textbook from Novato to San Francisco, but it costs $10 to ship it to Sacramento. It costs $15 to ship a textbook om Lodi to San Francisco, but it costs $4 to ship it from Lodi to Sacramento. The goal of the publisher is to minimize its total shipping cost. Formulate the problem with objective rnction and constraints Topic: Linear Programming 4. Osprey Machine Works has the following demand requirements and other data for the upcoming four quarters. Font er Demand Previous quarter's output 2500 units 2300 Beginning inventory 200 units 2400 Stockout (backorder) cost $50 per unit 2600 Inventory holding cost $10 per unit at end of quarter 2100 Hiring workers $4 per unit Laying off workers |$8 per unit What is the total cost of pursuing a level aggregate plan over the coming year? 5. Golden Eagle Machine Works has the following demand requirements and other data for the upcoming four quarters. Quarter Demand Previous quarter's output 2500 units 2300 Beginning inventory 200 units 2400 Stockout (backorder) cost $50 per unit 2600 Inventory holding cost $10 per unit at end of quarter 2100 Hiring workers $4 per unit Laying off workers $8 per unit What is the total cost of pursuing a chase aggregate plan over the coming year