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A town obtains its water supply from two wells, W1 and W2. The cost of securing water from each well is defined as follows:
CostW1 = 13 + 4Q1 + (Q1)2
CostW2 = 26 + 8Q2 + 4(Q2)2
Where Q1 and Q2 are the amount of water in million gallons per day (mgd) from each well.
The town needs a total of 2 mgd. The capacity of well 1 is 5 million gallons per day, and that of well 2 is 10 mgd. Using calculus (hint: calculus with substitution), determine the optimal amount of water that will be drawn from each well if the town wants to minimize total costs.
An insulated system contains two solid blocks in contact with each other; one hot and the other cold. After heat transfer over some time, thermal equilibrium is established in the container.
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The rigid bar AD is supported by two steel wires of (1/16)" diameter (E=29x10^6 psi) and a pin and bracket at D. Knowing that the wires were initially taut, determine (a) the additional tension in each wire when a 120-lb load P is applied at B
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