Firerock produces rubber used for tires by combining three ingredients: rubber, oil, and carbon black. The cost in cents per pound of each ingredient is given in Table 6.

The rubber used in automobile tires must have a hardness of between 25 and 35, an elasticity of at least 16, and a tensile strength of at least 12. To manufacture a set of four automobile tires, 100 pounds of product is needed. The rubber used to make a set of four tires must contain between 25 and 60 pounds of rubber and at least 50 pounds of carbon black. If we define R =pounds of rubber in mixture used to produce four tires O = pounds of oil in mixture used to produce four tires C = pounds of carbon black used to produce four tires then statistical analysis has shown that the hardness, elasticity, and tensile strength of a 100-pound mixture of rubber, oil, and carbon black is as follows:

Formulate an NLP whose solution will tell Firerock how to minimize the cost of producing the rubber product needed to manufacture a set of automobile tires.

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Tensile strength = 12.5.10(0) Elasticity Hardness = 17+.35R.04(0) 34 + .10R + .06(0) .001 (0) .002(R) .3(C) + .001(R)(0) + .005(0)2 + .001C