Imagine that a hypothetical life form is discovered on our moon and transported to earth. on a hot day, this life form begins to sweat, and it is determined that the heat of vaporization of its sweat is 241 cal/g. the scientist observing the extraterrestrial life form also begins to sweat. the heat of vaporization of the scientist's sweat is 580 cal/g at the skin's surface. if both the extraterrestrial life form and the scientist lose 186 g of sweat over the course of one hour, calculate the heat lost by each body from the vaporization of sweat.

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