Solve the Problem $x$ Televisions Are Manufactured and Sold Is as Follows

question 133

Multiple Choice

Solve the problem.
-A television manufacturing company has two different factories. The profit function for Factory I when $x$ televisions are manufactured and sold is as follows:
$$P ( x ) = - 0.07 x ^ { 2 } + 25 x - 250$$
The profit function for Factory II when $x$ televisions are manufactured and sold is as follows:
$$P ( x ) = - 0.075 x ^ { 2 } + 35 x - 1500$$
For what number of televisions is the profit the same at both factories, and what is the profit?

• A) 233 televisions; \(\$ 2583.33\)
• B) 134 televisions; \(\$ 1843\)
• C) 0 televisions; \(\$ 0\)
• D) 125 televisions; \(\$ 1781.25\)

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Definitions:

Perfect Information

A condition in decision making where all parties have full and identical information relevant to the decision.

Expected Payoff

The anticipated return of an investment or decision under uncertainty, calculated as a weighted average of all possible outcomes.

Posterior Probabilities

The probabilities of different possible outcomes or hypotheses being true after considering new evidence, rephrasing the concept in a broader context.

Prior Probabilities

The probabilities assigned to events before any new evidence is considered, often used in Bayesian analysis.