A line between a planet and the sun sweeps out two equal areas at different places as it moves along its orbit. Which factor remains constant as this happens?

a. the planet’s speed as it sweeps out the areas

b. the distance the planet moves along its orbit while it sweeps out the area

c. the time required to sweep out the areas

d. the distance from the sun to the planet while it sweeps out the areas

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