Suppose that a steel bridge, 1000 m long, were built without any expansion joints. suppose that only one end of the bridge was held fixed. what would the difference in the length of the bridge be between winter and summer, taking a typical winter temperature as 0°c, and a typical summer temperature as 40°c? the coefficient of thermal expansion of steel is 10.5 × 10-6 k-1.

The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern florida. to meet the monthly demand for electricity in these counties, which is given by the inverse demand function p = 1,200 – 4q, the utility company has set up two electric generating facilities: q1 kilowatts are produced at facility 1, and q2 kilowatts are produced at facility 2 (so q = q1 + q2). the costs of producing electricity at each facility are given by c1(q1) = 8,000 + 6q12 and c2(q2) = 6,000 + 3q22, respectively. determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profit