3. Consider the Reddy Mikks model of Example 2.1-1. Its optimal tableau is given in Example 3.3-1. If the daily availabilities of raw materials Ml and M2 are increased to 28 and 8 tons, respectively, use post-optimal analysis to determine the new optimal solution.

*4. The Ozark Farm has 20,000 broilers that are fed for 8 weeks before being marketed. The weekly feed per broiler varies according to the following schedule:

Week Iblbroiler 1

.26 2

.48 3

.75 4

1.00 5

1.30 6

1.60 7

1.90 8

2.10 For the broiler to reach a desired weight gain in 8 weeks, the feedstuffs must satisfy specific nutritional needs. Although a typical list of feedstuffs is large, for simplicity we will limit the model to three items only: limestone, corn, and soybean meaL The nutritional needs will also be limited to three types: calcium, protein, and fiber. The following table summarizes the nutritive content of the selected ingredients together with the cost data.

Content (Ib) per Ib of Ingredient Calcium Protein Fiber $ per lb Limestone .380 .00 .00 .12 Corn .001 .09 .02 .45 Soybean meal .002 .50 .08 1.60 The feed mix must contain

(a) At least .8% but not more than 1.2% calcium

(b) At least 22% protein

(c) At most 5% crude fiber Solve the LP for week 1 and then use post-optimal analysis to develop an optimal

. schedule for the remaining 7 weeks.

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4.5 Post-Optimal Analysis 185