Consider the following liner programming problem: Maximize and minimize Z= 110x+10y %3D Subject to: 9x+10y590 9х-5y20 y22 xy20

Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuation. Centerville is located at (9,0) in the xy-plane, Springfield is at (0,7), and Shelbyville is at (0, -7). The cable runs from Centerville to some point (a,0) on the ax-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (x, 0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer. To solve this problem we need to minimize the following function of a: f(x) = We find that f(x) has a critical number at a To verify that f(x) has a minimum at this critical number we compute the second derivative f"(x) and find that its value at the critical number is a positive number. Thus the…

Find the value of x

The graph shows the cost and revenue equations for a product. The x y-coordinate plane is given. The horizontal axis is labeled Number of units and the vertical axis is labeled Dollars . There are 2 lines on the graph. The line labeled C = 0.5x + 4,000 enters the window at y = 4,000 on the positive y-axis, goes up and right, passes through the point (10,000, 9,000) crossing the line labeled R = 0.9x, and exits the window in the first quadrant. The line labeled R = 0.9x enters the window at the origin, goes up and right, passes through the point (10,000, 9,000) crossing the line labeled C = 0.5x + 4,000, and exits the window in the first quadrant. (a) For what number of units sold does the company break even?   units (b) For what numbers of units sold is there a loss for the company? If less than   units are sold, the company loses money. (c) For what numbers of units sold is there a profit for the company? If more than   units are sold, the company makes a profit.

Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuation. Centerville is located at (10, 0) in the xy-plane, Springfield is at (0, 9), and Shelbyville is at (0, – 9). The cable runs from Centerville to some point (x, 0) on the r-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (x, 0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer. To solve this problem we need to minimize the following function of r: f(x) = We find that f(x) has a critical number at r = To verify that f(x) has a minimum at this critical number we compute the second derivative f''(x) and find that its value at the critical number is , a positive number. Thus…

Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y- shaped configuation. Centerville is located at (7, 0) in the xy-plane, Springfield is at (0, 5), and Shelbyville is at (0, The cable runs from Centerville to some point (x, 0) on 5). the x-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (x, 0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer. To solve this problem we need to minimize the following function of : f(x) = Preview We find that f(x) has a critical number at x = Preview To verify that f (x) has a minimum at this critical number we compute the second derivative f''(x) and find that its value at the critical number is Preview a…

Reply as soon as posible. Consider the rectangle RSPQ inscribed in the parallelogram BADC, shown below.below (the figure shows the equations of the lines that gave rise to the parallelogram): (the figure is in the pictures) Let (x, y) be the coordinates of point P. We want to find the values ​​of x and y such that the areaof the RSAPQ pentagon is as high as possible. An objective function in the variables x and y, which allowssolve the problem is: A) A(x, y) = xy + 10xB) A(x, y) = 4xy + (xy/2)C) A(x, y) = 3xy + 10xD) A(x, y) = 2xy + 20x