Construct a mathematical model in the form of a linear programming problem.  Then solve the problem by the simplex, dual problem, or big M methods.

A company blends long-grain rice and wild rice to produce two brands of rice mixes: brand A, which is marketed under the company’s name, and brand B, which is marketed as a generic brand. Brand A must contain at least 10% wild rice, and brand B must contain at least 5% wild rice. Long-grain rice costs $0.70 per pound, and wild rice costs $3.40 per pound. The company sells brand A for $1.50 a pound and brand B for $1.20 a pound. The company has 8,000 pounds of long-grain rice and 500 pounds of wild rice on hand. How should the company use the available rice to maximize its profit? What is the maximum profit?