document.write( "Question 1165007: The Cream and Custard Bakery makes both coffee cakes and Danish in large pans. The main
\n" ); document.write( "ingredients are flour and sugar. There are 25 pounds of flour and 16 pounds of sugar available
\n" ); document.write( "and the maximum demand for coffee cakes is 8. Five pounds of flour and 2 pounds of sugar
\n" ); document.write( "are required to make one pan of coffee cake, and 5 pounds of flour and 4 pounds of sugar are
\n" ); document.write( "required to make one pan of Danish. One pan of coffee cake has a profit of PhP 1, and one pan
\n" ); document.write( "of Danish has a profit of PhP 5. Determine the number of pans of cake and Danish that the
\n" ); document.write( "bakery must produce each day so that profit will be maximized. \n" ); document.write( "
Algebra.Com's Answer #851818 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "The Cream and Custard Bakery makes both coffee cakes and Danish in large pans. The main
\n" ); document.write( "ingredients are flour and sugar. There are 25 pounds of flour and 16 pounds of sugar available
\n" ); document.write( "and the maximum demand for coffee cakes is 8. Five pounds of flour and 2 pounds of sugar
\n" ); document.write( "are required to make one pan of coffee cake, and 5 pounds of flour and 4 pounds of sugar are
\n" ); document.write( "required to make one pan of Danish. One pan of coffee cake has a profit of PhP 1, and one pan
\n" ); document.write( "of Danish has a profit of PhP 5. Determine the number of pans of cake and Danish that the
\n" ); document.write( "bakery must produce each day so that profit will be maximized.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        This problem is simple: it is accessible to a third-grader.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        Therefore, I will not write a standard solution using Linear programming method,\r
\n" ); document.write( "\n" ); document.write( "        but will show a simple arithmetic solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "From the problem, it is clear that the maximum number of cakes is 5.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Indeed, the bakery can make 5  coffee cakes, using 5*5 = 25 pounds of flour and 5*2 = 10 pounds of sugar.\r\n" );
document.write( "It can not make more than 5 cakes, either coffee cakes or Danish.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, our task is to make a schedule (a Table) showing possible cakes that can be prepared, and possible profit.\r\n" );
document.write( "Obviously, we should spend as much of the ingredients as allowed by restrictions.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Also, from the given data, it is obvious, that for any given number of total cakes, the bakery should \r\n" );
document.write( "make as many Danish pans as possible, then adding coffee cakes until fitting the restrictions.\r\n" );
document.write( "\r\n" );
document.write( "It is because the first limiting restriction is the amount of floor, and regarding the floor, \r\n" );
document.write( "the coffee cakes and the Danish pans are in equal position, while Danish provides greater profit.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "   the number   coffee   Danish    Floor         Sugar           Profit\r\n" );
document.write( "    of cakes    cakes     pans                                   (Php)\r\n" );
document.write( "    (total)\r\n" );
document.write( " --------------------------------------------------------------------------\r\n" );
document.write( "       5          5        0      5*5 = 25      5*2 = 10        5*1 =  5\r\n" );
document.write( "\r\n" );
document.write( "       4          0        4      0*5+4*5 = 20  0*2+4*4 = 16    4*5 = 20      (*)\r\n" );
document.write( "\r\n" );
document.write( "       4          1        3      1*5+3*5 = 20                  1+3*5 = 16\r\n" );
document.write( "\r\n" );
document.write( "       4          2        2      2*5+2*5 = 20  2*2+2*4 = 12    2*2+2*4 = 12\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "There is no sense to continue the table further.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Looking into the table, we mark the optimum solution by (*).\r\n" );
document.write( "It provides the maximum profit of  Php 20 .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  4 Danish pans and 0 (zero) coffee cakes satisfy the restrictions and provide the maximum profit of Php 20.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );