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Name: Date: Period: Algebra 2, Chapter 3, Section 4: Linear Programming 1. A business makes FRHS hats in green and black. The business can only produce at most 250 hats per day. Hat materials cost $4 per green hat and $6 per black hat. The business budgets $1200 per day for material expenses. Each green hat sells for $16 and each black hat sells for $20. How many of each hat should the business produce in order to maximize daily income? (a) Define your variables and write a system of linear inequalities to represent the business constraints. (b) Graph the feasible region. (c) Determine the objective function, find all vertices, and tabulate the income possible at each point. Vertex (x, y) Income Objective Function: _____________________ (d) How much of each kind of hat should the business produce in order to maximize daily income? 2. A farmer has 90 acres available for planting millet and alfalfa. Seed costs $4 per acre for millet and $6 per acre for alfalfa. Labor costs are $20 and acre for millet and $10 an acre for alfalfa. The farmer intends to spend no more than $480 for seed and $1400 for labor. The expected income is $110 per acre for millet and $150 per acre for alfalfa. (a) Define your variables and write a system of linear inequalities to represent the farmer’s constraints. (b) Graph the feasible region. (c) Determine the objective function, find all vertices, and tabulate the income possible at each point. Vertex (x, y) Objective Function: ___________________________ (d) How much of each crop should the farmer plant in order to maximize income? Income