Have you ever wondered how scientists are able to form hypotheses and make new discoveries? The scientific method is a basic tool that guides you through solving a problem. In this activity, you will put the scientific method to the test. You will first solve a provided problem.    Imagine that you flick a light switch, but the lightbulb fails to turn on. What could cause this malfunction?  For this problem, include these components:  ∗the problem you have observed  ∗a hypothesis  ∗an experiment to test your hypothesis  ∗data or results of your experiment (hypothetical data)  ∗a statement in which you accept or reject your hypothesis

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