Use a graphing calculator or a computer program for the simplex method to solve this linear programming problem. x1 x2 x3 x4 s1 s2 $3 0. 375 .625 510 75 .5 .375 1 600 1 25 125 0. 1 290 -90 -65 -60 -50 The optimal solution X1= X2= X3= X4= produces the maximum value (Do not round until the final answer. Then round to the nearest integer as needed.

For a certain company, the cost for producing a items is 40x + 300 and the revenue for selling x items is 80x – 0.5x². The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit! Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.) Part b: Find two values of that will create a profit of $50. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or x + 1; x – 1). The order of the list does not matter. To enter va , type sqrt(a).

A business owner is monitoring the production cost of making laptop computers. It costs $5,000 to start the business. The production cost for 10 computers totals $6,000, and the production cost for 20 computers totals $5,000. Which type of function would best model the data, and why? Quadratic, because the production cost decreases to a minimum of $5,000 and then increases Quadratic, because the production cost increases to a maximum of $5,000 and then decreases Quadratic, because the production cost decreases to a minimum of $6,000 and then increases Quadratic, because the production cost increases to a maximum of $6,000 and then decreases

Social networking and video-sharing sites often include rich media and display advertising placed around user- generated content. Suppose that, for a particular social networking company, the annual revenue R, in millions of dollars, from rich media advertisements for the five years from the beginning of 2015 through the end of 2019 can be approximated by the model $ R(x) = x¹ + 11x³ - 39x² + 45x, where a is the number of years from the beginning of 2015. What was the total revenue for this company in the five-year period? Round to 2 decimal places. million -