Hannah just finished building a house of cards that stands four stories high. she is worried that it will fall down. which of the following statements must be true?
if no unbalanced force acts upon the house of cards, then it will remain standing forever.
as long as nobody touches the house of cards, it will remain standing.
if hannah adds another card to the house of cards, then it will fall down.
a house of cards is too fragile and must fall down eventually due to gravity.

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