Two chemicals can be produced at one facility, and each takes one hour per ton to produce. Both…

 Two chemicals can be produced at one facility, and each takes one hour per ton to produce. Both exhibit diseconomies of scale: If x1 tons of the first are produced, the contribution is 6×1 − (x 2 1 /2); for the second chemical, the contribution is √ 50×2 for x2 tons produced. The facility can work 23 hours per day (one hour is required for maintenance) and, because of raw materials availability, no more than 10 tons of the first chemical and 18 tons of the second can be produced daily. What is the optimal daily production schedule, to maximize contribution?

 Solve by separable programming, using the δ-method described in Chapter 9. For x1 use a grid: 0, 3, 6, 10, and for x2 use a grid 0, 2, 5, 18.

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