document.write( "Question 1203984: A company produces two products, A and B. The sales volume for A is at least 80% of the total sales of both A and B. However, the company cannot sell more than 100 unit of A per day. Both products use one raw material whose maximum daily availability is limited to 240 lb a day. The usage rates of the raw material are 2 lb per unit of A and 4 lb per unit of B. The unit prices for A and B are $20 and $50, respectively. Determine the optimal product mix for the company.\r
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Algebra.Com's Answer #839947 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A company produces two products, A and B. The sales volume for A is at least 80%
\n" ); document.write( "of the total sales of both A and B. However, the company cannot sell more than 100 unit of A per day.
\n" ); document.write( "Both products use one raw material whose maximum daily availability is limited to 240 lb a day.
\n" ); document.write( "The usage rates of the raw material are 2 lb per unit of A and 4 lb per unit of B.
\n" ); document.write( "The unit prices for A and B are $20 and $50, respectively.
\n" ); document.write( "Determine the optimal product mix for the company.
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document.write( "Looking at the unit prices ($20 per A and $50 per B), you start think that the best strategy\r\n" );
document.write( "is to make as many of products B as possible.\r\n" );
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document.write( "Looking at the usage rate of the raw material (2 lb for A and 4 lb for B) and comparing it \r\n" );
document.write( "with the unit prices, you only become stronger in your opinion.\r\n" );
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document.write( "So, the optimal strategy is (a) to produce as many Bs as possible; \r\n" );
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document.write( "                            (b) to make as few As as needed by the restriction A >= 0.8(A+B),\r\n" );
document.write( "                                which gives  A = ~ 4B.\r\n" );
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document.write( "                            (c) then to spend the rest of the raw material (if any) to make As, \r\n" );
document.write( "                                still remaining under this restriction A >= 4B.\r\n" );
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document.write( "Let's calculate the number of As and Bs. Write an inequality for the raw material\r\n" );
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document.write( "    2A + 4B <= 240 lbs.\r\n" );
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document.write( "Use A = 4B.  You will get\r\n" );
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document.write( "    2*(4B) + 4B <= 240\r\n" );
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document.write( "    8B + 4B <= 240\r\n" );
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document.write( "      12B   <= 240  --->  B <= 240/12 = 20.\r\n" );
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document.write( "So, make 20 Bs and 4*10 = 80 As.  You will spend  2*80 + 4*20 = 160 + 80 = 240 lbs of the raw material.\r\n" );
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document.write( "                                  so, you will spend ALL the raw material.\r\n" );
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document.write( "All other restrictions will be satisfied.  The problem is just solved (using mental reasoning).\r\n" );
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document.write( "ANSWER.  The optimal strategy is to make 80 As and 20 Bs.\r\n" );
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