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 configuration. Centerville is located at (15,0) in the xy-plane, Springfield is at (0,3), and Shelbyville is at (0,-3). The cable runs from Centerville to some point (x,0) on the x-axis where it splits into two branches going to Springfield and Shelbyville. (Draw a picture of this situation). It costs $1000 per unit to lay cable along the x-axis and $1250 per unit otherwise. Write a function for the total cost of laying the cable in terms of x. Cost(x)=__________ Take the derivative of your cost function by carefully applying the chain rule. dCost/dx=__________ To find the x location that yields a minimum cost we need Calculus! Recall that if the derivative of the cost function is zero then the x is sitting at a possible maximum or minimum. Set your derivative to zero and carefully do the algebra to solve for the critical point x. Critical Point: x=__________miles.
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 configuration. Centerville is located at (15,0) in the xy-plane, Springfield is at (0,3), and Shelbyville is at (0,-3). The cable runs from Centerville to some point (x,0) on the x-axis where it splits into two branches going to Springfield and Shelbyville. (Draw a picture of this situation).
It costs $1000 per unit to lay cable along the x-axis and $1250 per unit otherwise.
Write a function for the total cost of laying the cable in terms of x.
Cost(x)=__________
Take the derivative of your cost function by carefully applying the chain rule.
dCost/dx=__________
To find the x location that yields a minimum cost we need Calculus! Recall that if the derivative of the cost function is zero then the x is sitting at a possible maximum or minimum. Set your derivative to zero and carefully do the algebra to solve for the critical point x.
Critical Point: x=__________miles.
Now that you have the critical point, use it in the original cost function to find the minimized cost.
Minimized Cost = $__________.
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