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This question tests the student's ability to model and solve Integer Programming problems

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A patient’s doctor advises her to buy two types of pills that will replenish the deficiency of vitamin A, potassium and beta carotene in her diet. Each type of Pill I contains {v201} units of vitamin A, {p151} units of potassium, {b61} units of beta carotene, and costs {c0131} \\$. Each type of Pill II contains {v151} unit of vitamin A, {p301} units of potassium, {b201} units of beta carotene, and costs {c0171} \\$. The patient needs a minimum of {v22501} units of vitamin A, a minimum of {p30001} units of potassium and a minimum of {b16001} units of beta carotene. She wishes to minimize the cost of the pills.

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Formulate the linear programming problem using variables x1 (for $x_1$ Pill I), ...

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Put \">=\" for \"$\\ge$\" and \"<=\" for \"$\\le$\".

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A. Objective:[[0]] [[1]]

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B. Give the system of constraints:

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for vitamin A: [[2]]$\\ge$[[10]]

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for potassium: [[3]]$\\ge$[[11]]

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for beta carotene [[4]]$\\ge$[[12]]

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C. Range of varables:

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$x_1$ is [[5]]  

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$x_2$ is [[6]]

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D. Optimal solution: $x_1$ = [[7]],  $x_1$ = [[8]]

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E. Minimal cost: [[9]]

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