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    <p>You want to optimize the following function</p> <pre><code>$cost = $amountOfProductA * $costOfProductA + $amountOfProductB * $costOfProductB + $amountOfProductC * $costOfProductC </code></pre> <p>With the following restriction</p> <pre><code>$powerDeliveredByA * $amountOfProductA + $powerDeliveredByB * $amountOfProductB + $powerDeliveredByC * $amountOfProductC = 65 </code></pre> <p>So these lines find solutions that yield 65 (or close to 65, using an acceptable threshold you'd have to set), then sort the solutions array by the cost, and get the first element of the solutions array:</p> <pre><code>$requiredPower = 65; $productA = array('amount' =&gt; 0, 'cost' =&gt; 50, 'powerDelivered' =&gt; 5); $productB = array('amount' =&gt; 0, 'cost' =&gt; 80, 'powerDelivered' =&gt; 9); $productC = array('amount' =&gt; 0, 'cost' =&gt; 140, 'powerDelivered' =&gt; 15); $increment = 0.01; $threshold = 0.01; $solutions = array(); while($productA['amount'] * $productA['powerDelivered'] &lt; $requiredPower) { $productC['amount'] = 0; while($productB['amount'] * $productB['powerDelivered'] &lt; $requiredPower) { $productC['amount'] = 0; while($productC['amount'] * $productC['powerDelivered'] &lt; $requiredPower) { if($productA['amount'] * $productA['powerDelivered'] + $productB['amount'] * $productB['powerDelivered'] + $productC['amount'] * $productC['powerDelivered'] &gt; $requiredPower + $threshold) { break; } if(isWithinThreshold($productA['powerDelivered'] * $productA['amount'] + $productB['powerDelivered'] * $productB['amount'] + $productC['powerDelivered'] * $productC['amount'], $requiredPower, $threshold)) { //var_dump($productA['powerDelivered'] * $productA['amount'] + $productB['powerDelivered'] * $productB['amount'] + $productC['powerDelivered'] * $productC['amount']); $cost = $productA['amount'] * $productA['cost'] + $productB['amount'] * $productB['cost'] + $productC['amount'] * $productC['cost']; $solutions[number_format($cost,10,'.','')] = array('cost' =&gt; $cost, 'qA' =&gt; $productA['amount'], 'qB' =&gt; $productB['amount'], 'qC' =&gt; $productC['amount']); } $productC['amount'] = $productC['amount'] + $increment; } $productB['amount'] = $productB['amount'] + $increment; } $productA['amount'] = $productA['amount'] + $increment; } ksort($solutions, SORT_NUMERIC); $minimumCost = array_shift($solutions); var_dump($minimumCost); //checks if $value1 is within $value2 +- $threshold function isWithinThreshold($value1, $value2, $threshold) { if($value1 &gt;= $value2 - $threshold &amp;&amp; $value1 &lt;= $value2 + $threshold) { return true; } } </code></pre> <p>The way to optimize a function is described here: <a href="http://en.wikipedia.org/wiki/Knapsack_problem" rel="nofollow">Function Optimization</a></p>
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    1. POCalculate which products together would deliver the requested power
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    1. USDiego Saa
    1. USDiego Saa
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    1. COThis doesn't actually answer the question.
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      1. USSomeKittens
    2. COThe optimization is easy in that case. 0, 0, 0. You don't take the $requiredPower here into account.
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      1. USMadara Uchiha
    3. COThat link doesn't offer any help for discretized solutions other than saying they are harder.
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      1. USwalrii
 

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