1. Graphically determine the minimum value of the function

1. Graphically determine the minimum value of the function f(x, y) = 3x + 5y subject to the constraints 3x + 2y ≥ 36, 3x + 5y ≥ 45, x ≥ 0, y ≥ 0. Determine all the points in the feasible region at which the minimum value is attained. 2. A pet food manufacturer produces two types of food: regular and premium. A 20kg bag of regular food requires 2 hours to prepare and 3 hours to cook; a 20kg bag of premium food requires 2 hours to prepare and 5 hours to cook. The materials used to prepare the food are available 8 hours per day and the oven used to cook the food is available 15 hours per day. The profit on a 20kg bag of regular food is $42 and a 20kg bag of premium food is $50. Determine how many bags of each type of food should be made to maximise the profit (fractional bags can be produced – they just sell them in smaller bags).

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