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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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Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Hac habitasse platea dictumst vestibulum rhoncus est pellentesque. Amet dictum sit amet justo donec enim diam vulputate ut. Neque convallis a cras semper auctor neque vitae. Elit at imperdiet dui accumsan. Nisl condimentum id venenatis a condimentum vitae sapien pellentesque. Imperdiet massa tincidunt nunc pulvinar sapien et ligula. Malesuada fames ac turpis egestas maecenas pharetra convallis posuere. Et ultrices neque ornare aenean euismod. Suscipit tellus mauris a diam maecenas sed enim. Potenti nullam ac tortor vitae purus faucibus ornare. Morbi tristique senectus et netus et malesuada. Morbi tristique senectus et netus et malesuada. Tellus pellentesque eu tincidunt tortor aliquam. Sit amet purus gravida quis blandit. Nec feugiat in fermentum posuere urna. Vel orci porta non pulvinar neque laoreet suspendisse interdum. Ultricies tristique nulla aliquet enim tortor at auctor urna. Orci sagittis eu volutpat odio facilisis mauris sit amet.

Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.

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MX3536 Differential Equations

Question Partial Differential equations 1.(a) Find characteristics for the PDE describing u(t, x) for t ∈ R and x ∈ R Hence find the general solution.(b) Find the solution that satisfies the initial conditions      2. Consider the following equation for u(x,y)   (a) Assuming x 6=0cl ...

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MHF4U1 advanced functions

Instructions Please complete each of the following questions and submit your work to the associated dropbox, located on the HUB. Please include diagrams and show your work to receive full marks. 1. Complete each of the following: a) Create a table of values and sketch a graph of the following ...

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Human Development Index (HDI)

Task: The calculation of a geometric (i.e. multiplicative) mean of income, education and life expectancy components in the UNDP’s Human Development Index (HDI) provides a more appropriate indication of ‘development’ than the arithmetic (i.e. additive) combinations of components in ...

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