3. (Use the graphical method for the following problem): A technology company manufac- tures televisions and soundbars. The following table gives the labor requirements and profits per automobile: TelevisionsSoundbars Assemble10 labor-hours8 labor-hours Load and Transport2 labor-hours1 labor-hours Profit$150$100 Each day, 360 labor-hours are available to assemble these products and 60 labor-hours are avail- able to load and trasport them. The manufacturer wants to determine how many televisions and soundbars to produce of each type in order to maximize profit under these constraints. (a)[5 points]Define variables for modeling this scenario, and write down the objective function.

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(b) Identify the constraints of the problem.

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Assembly: 10x+ 8y≤360, Load and Transport: 2x+y≤60, We also have our physical constraints (no negative items can be produced): x≥0, y≥0. The complete system of constraints is given by 10x+ 8y≤360 2x+y≤60 x≥0, y≥0 (c) List the corner points of the feasible region.

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Thus the corner points are (0,0),(0,45),(20,20),(30,0). (d)[5 points]How many televisions and soundbars should be produced each day to maximize the total profit?

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4. A colleague approaches you with the following simplex tableau: xyzstup 050140072 100031060 111010022 3-200-401140 (a)[10 points]Your colleague does not remember which variables to list in the first column of the tableau. Write down these variables, and give their values.

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