A group of college students are starting a small business called Custom Tech. They make customized cell phone and tablet cases. Their profits are $40 for the cell phone case and$60 for the tablet case. The process involves both design hours and manufacturing hours. It takes 0.5 hour to design and 0.3 hour to manufacture a customized phone case. It takes 0.4 hour to design and 0.4 hour to manufacture a customized tablet case. Since the design part is completed by students attending school, they can allocate no more than 100 hours per day for design. They are sharing a single manufacturing machine with another company and only have 8 hours per day to use it. Let x represent the number of customized cell phone cases and y represent the number of customized tablet cases. Write the design constraint inequality.

A group of college students are starting a small business called Custom Tech. They make customized cell phone and tablet cases. Their profits are $40 for the cell phone case and$60 for the tablet case. The process involves both design hours and manufacturing hours. It takes 0.5 hour to design and 0.3 hour to manufacture a customized phone case. It takes 0.4 hour to design and 0.4 hour to manufacture a customized tablet case. Since the design part is completed by students attending school, they can allocate no more than 100 hours per day for design. They are sharing a single manufacturing machine with another company and only have 8 hours per day to use it. Let x represent the number of customized cell phone cases and y represent the number of customized tablet cases. Write the profit objective function.

Solve each problem, if possible. If not possible, state whether the problem is infeasible, has alternate optimal solutions, or is unbounded. Agriculture The county officials in Chang Qing County, China used linear programming to aid the farmers in their choices of crops and other forms of agricultural production. This led to a 12% increase in crop profits, a 54% increase in animal husbandry profits, while improving the region's ecology. Suppose an American farmer has 180 acres on which to grow corn and soybeans. He is planting at least 40 acres of corn and 20 acres of soybeans. Based on his calculations, he can earn $150 per acre of corn and$250 per acre of soybeans. If the farmer plants at least 2 acres of corn for every acre of soybeans, how many acres of each should he plant to earn the greatest profit?