Let's say we are producing two products, pi and p2, by using two raw materials, r1 and r2. To make one unit of p1, we use 1 unit of r1, 2 units of r2 and to make one unit of p2, we use 3 units of r1, 2 units of r2. Value of one unit of rı is $1 and value of one unit of r2 is $3 and we have a total of 100 units of r1 and 200 units of r2. Let the selling price per one pi made be $10 and per one p2 made be $15. We want to maximize the profit.

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
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Set up a utlitiy maximization problem given the following information. 

Let's say we are producing two products, \( p_1 \) and \( p_2 \), by using two raw materials, \( r_1 \) and \( r_2 \). To make one unit of \( p_1 \), we use 1 unit of \( r_1 \), 2 units of \( r_2 \), and to make one unit of \( p_2 \), we use 3 units of \( r_1 \), 2 units of \( r_2 \). The value of one unit of \( r_1 \) is $1 and the value of one unit of \( r_2 \) is $3. We have a total of 100 units of \( r_1 \) and 200 units of \( r_2 \). Let the selling price per unit of \( p_1 \) be $10 and per unit of \( p_2 \) be $15. We want to maximize the profit.
Transcribed Image Text:Let's say we are producing two products, \( p_1 \) and \( p_2 \), by using two raw materials, \( r_1 \) and \( r_2 \). To make one unit of \( p_1 \), we use 1 unit of \( r_1 \), 2 units of \( r_2 \), and to make one unit of \( p_2 \), we use 3 units of \( r_1 \), 2 units of \( r_2 \). The value of one unit of \( r_1 \) is $1 and the value of one unit of \( r_2 \) is $3. We have a total of 100 units of \( r_1 \) and 200 units of \( r_2 \). Let the selling price per unit of \( p_1 \) be $10 and per unit of \( p_2 \) be $15. We want to maximize the profit.
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