Use a Graphing Calculator to Solve the Nonlinear System $x$ Are Manufactured and Sold Is as Follows

question 304

Multiple Choice

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth.
-A chair manufacturing company has two different factories. The profit function for Factory I when $x$ are manufactured and sold is as follows:
$$P ( x ) = - 0.05 x ^ { 2 } + 20 x - 500$$
The profit function for Factory II when $x$ chairs are manufactured and sold is as follows:
$$P ( x ) = - 0.05 x ^ { 2 } + 30 x - 2500$$
For what number of chairs is the profit the same at both factories, and what is the profit?

• A) 100 chairs; \(\$ 1000\)
• B) 0 chairs; \(\$ 0\)
• C) 300 chairs; \(\$ 2000\)
• D) 200 chairs; \(\$ 1500\) hairs300)

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Definitions:

Assignable

Refers to the capability of transferring rights or interests in a contract or financial instrument to another party.

Revoked

The act of officially canceling or rescinding a legal right, license, permission, or privilege.

Firm Offer

A binding proposal to sell or buy goods that holds the offering party to its terms for a certain period.

Merchant

An individual or company engaged in the business of buying and selling goods for profit.