Maximize $p = 2 x + 3 y + z + 4 w$

question 143

Multiple Choice

Maximize $p = 2 x + 3 y + z + 4 w$
Subject to
$\begin{aligned}x + y + z + w & \leq 40 \\2 x + y - z - w & \geq 10 \\x + y + z + w & \geq 10 \\x \geq 0 , y \geq 0 , z \geq 0 , w & \geq 0\end{aligned}$

• A) \(p = 65\) , \(x = 25\) , \(y = 0\) , \(z = 15\) , \(w = 0\)
• B) \(p = 135\) , \(x = 0\) , \(y = 25\) , \(z = 0\) , \(w = 15\)
• C) \(p = 130\) , \(x = 0\) , \(y = 15\) , \(z = 0\) , \(w = 15\)
• D) \(p = 55\) , \(x = 15\) , \(y = 0\) , \(z = 25\) , \(w = 0\)
• E) no solution

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Definitions:

Supply Curve

An illustrated chart depicting the correlation between the cost of a commodity and the volume of the commodity sellers aim to provide.

Supply Factor

An influence that affects the quantity of a product or service that suppliers are willing and able to sell in the market at a given price level.

Health Care Market

The aggregation of all entities (providers, payers, and patients) involved in the production, distribution, and consumption of health care services.

Productivity Growth

The rate at which an economy's or an industry's output per unit of input (labor, capital, etc.) increases over time, indicating improvement in efficiency.