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A store sells two models of laptop computers. Because of the demand, the store stocks at least twice as many units of model \( A \) as of model \( B \). The costs to the store for the two models are \( \$800 \) and \( \$1200 \), respectively. The management does not want more than \( \$20,000 \) in computer inventory at any one time, and it wants at least four model \( A \) laptop computers and two model \( B \) laptop computers in inventory at all times. Find and graph a system of inequalities describing all possible inventory levels.

For a concert event, there are \( \$30 \) reserved seat tickets and \( \$20 \) general admission tickets. There are 2000 reserved seats available, and fire regulations limit the number of paid ticket holders to 3000. The promoter must take in at least \( \$75,000 \) in ticket sales. Find and graph a system of inequalities describing the different numbers of tickets that can be sold.

A warehouse supervisor is told to ship at least 50 packages of gravel that weigh 55 pounds each and at least 40 bags of stone that weigh 70 pounds each. The maximum weight capacity of the truck to be used is 7500 pounds. Find and graph a system of inequalities describing the numbers of bags of stone and gravel that can be shipped.

A dietitian is asked to design a special dietary supplement using two different foods. Each ounce of food \( X \) contains 20 units of calcium, 15 units of iron, and 10 units of vitamin \( B \). Each ounce of food \( Y \) contains 10 units of calcium, 10 units of iron, and 20 units of vitamin \( B \). The minimum daily requirements of the diet are 300 units of calcium, 150 units of iron, and 200 units of vitamin \( B \). (a) Write a system of inequalities describing the different amounts of food \( X \) and food \( Y \) that can be used. (b) Sketch a graph of the region corresponding to the system in part (a). (c) Find two solutions of the system and interpret their meanings in the context of the problem.