2) Alexis Cornby makes her living buying and selling corn. On January 1s, she ha

Question

2) Alexis Cornby makes her living buying and selling corn. On January 1s, she has 50 tons of corn and S1,000 Alexis can buy corn on the first day of cach month and sell corn on the last day of cach month at the prices shown in Table 3. Alexis stores her corn in a warehouse that can hold at most 100 tons of corn. She must be able to pay cash for all corn at the time of purchase a) Formulate a linear programming model to determine how Alexis can maximize her cash on hand at the end of December. b) Solve the linear program using the IBM ILOG CPLEX Optimization Studio Table 3-Corn Purehase and Selling Prices Selling Price (S/ton) 250 400 350 550 300 Purchase Price (S/ton) 250 550 400 350 400 250 Selling Price (S/ton) 500 550 350 650 700 400 Month Purchase Price Month January February March April May une (S/ton) 300 350 400 500 200 600 July August September October November December

Explanation / Answer

Answer:Linear programming Model Decision Variables

Initial balance in tons 50 50+x1-y1 50+x1-y1+x2-y2 50+x1-y1+x2-y2+x3-y3
Amount bought x1 x2 x3 x4
Amount sold y1 y2 y3 y4
Ending Balance 50+x1-y1 50+x1-y1+x2-y2 50+x1-y1+x2-y2+x3-y3 50+x1-y1+x2-y2+x3-y3+x4-y4 Cost 300 350 400 500
Selling price 250 400 350 550  
Initial balance in money $ 1,000.00 1000+250y1-350x1 1000+250y1+400y1-300x1-350x2 1000+250y1+400y1+350y3-300x1-350x2-400x3
Money spent 300x1 x2 x3 x4
Money received 250y1 y2 y3 y4
Ending Balance 1000+250y1-300x1 1000+250y1+400y1-300x1-350x2 1000+250y1+400y1+350y3-300x1-350x2-400x3 1000+250y1+400y1+350y3+550y4-300x1-350x2-400x3-500x4

Objective function is to Maximize ending balance 1000+ 250y1+ 400y1 +350y3 +550y4 -300x1 -350x2 -400x3 -500x4
Constraints Amount at end of each month should be less than 100tons 50+x1-y1 <= 100 50+x1-y1+x2-y2 <= 100 50+x1-y1+x2-y2+x3-y3 <= 100 50+x1-y1+x2-y2+x3-y3+x4-y4 <= 100
Ending balance must be gretaer than zero 50+x1-y1 >= 0 50+x1-y1+x2-y2 >= 0 50+x1-y1+x2-y2+x3-y3 >= 0 50+x1-y1+x2-y2+x3-y3+x4-y4 >= 0...

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