Two products are manufactured sequentially on tow machines. The time available on each machine is 8 hours

Two products are manufactured sequentially on tow machines. The time available on each machine is 8 hours per day and may be increased by up to 4 hours of overtime, if necessary, at an additional cost of $100 per hour.

Develop an LP Model to determine the optimum production schedule and the recommended use of overtime, if any. Solve using AMPL.
Shelf Space Allocation. A grocery store must decide on the shelf space to be allocated to each of five types of breakfast cereals. The maximum daily demand is 100, 85, 140, 80 and 90 boxes, respectively. The shelf space in square inches for the respective boxes is 16, 24, 18, 22 and 20. The total available shelf space is 5000 in^2. The profit per unit is $1.10, $1.30, $1.08, $1.25 and $1.20 respectively. Determine the optimal space allocation for the five cereals. Use AMPL to solve.
A refinery manufactures two grades of jet fuel, F1 and F2, by blending four types of gasoline, A, B, C, and D. Fuel F1 uses gasolines A, B, C and D in the ratio 1:1:2:4, and fuel F2 uses the ratio 2:2:1:3. The supply limits for A, B, C, and D are 1000, 1200, 900 and 1500 bbl/day, respectively. The costs per bbl for gasolines A, B, C, and D are $120, $90, $100 and $150, respectively. Fuels F1 and F2 sell for $200 and $250 per bbl, respectively. The minimum demand for F1 and F2 is 200 and 400 bbl/day, respectively. Develop an LP model to determine the optimal production mix for F1 and F2, and find the solution using AMPL.

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