document.write( "Question 1142242: It takes 10 units of carbohydrates and 4 units of protein to satisfy Jacob's minimum weekly requirements. The meat contains 2 units of carbohydrates and 2 units of protein per pound. The cheese contains 3 units of carbohydrates and 1 unit of protein per pound. The meat costs $3.20 per pound and the cheese costs $4.70 per pound. How many pounds of each are needed to fulfill the minimum requirements at minimum cost? What is Jacob's minimum cost?
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Algebra.Com's Answer #762949 by ikleyn(52797) $\"\"$ $\"About$

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document.write( "From the condition, you have these two equations in two unknowns\r\n" );
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document.write( "    2M + 3C = 10  units of carbohydrates    (1)\r\n" );
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document.write( "    2M + 1C =  4  units of protein          (2)\r\n" );
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document.write( "where M is the amount of Meat in pounds and C is the amount of Cheese in pounds.\r\n" );
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document.write( "To solve the system, use the Elimination method. For it, subtract eq(2) from eq(1). You will get\r\n" );
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document.write( "    3C - 1C = 10 - 4\r\n" );
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document.write( "    2C      =  6\r\n" );
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document.write( "     C      = 6/2 = 3 pounds of cheese.\r\n" );
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document.write( "Then from eq(2) you get\r\n" );
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document.write( "    2M + 3 = 4,\r\n" );
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document.write( "which implies  \r\n" );
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document.write( "    2M = 4 - 1 = 1  =====>  M = 0.5  pounds of meat.\r\n" );
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document.write( "So, Jacob's minimum need is  0.5 of a pound of meat and  3 pounds of cheese weekly,  ACCORDING TO THE SOLUTION.   ANSWER 1\r\n" );
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document.write( "The cost of this food is  \r\n" );
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document.write( "    3.20*0.5 + 4.70*3 dollars = 15.70 dollars.     ANSWER 2\r\n" );
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\n" ); document.write( "\n" ); document.write( "Again:   the solution is in two steps.\r
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\n" ); document.write( "\n" ); document.write( "First step is to find the amounts of ingredients required.\r
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\n" ); document.write( "\n" ); document.write( "The second step is to calculate the total cost of the food.\r
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\n" ); document.write( "\n" ); document.write( "Although the word \"mimimum\" occurs many times in the text of the problem, this problem is not
\n" ); document.write( "a \"minimization type\" of problems. It is on \"solving systems of linear equations\".
\n" ); document.write( "It is important to distinct between these two different types of problems.\r
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\n" ); document.write( "\n" ); document.write( "If you want to see other similar solved problems, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Counting calories and grams of fat in combined food\r
\n" ); document.write( "\n" ); document.write( "    - Solving word problems by reducing to systems of linear equations in three unknowns,   Problem 3\r
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