In the context of planning a training program, even though it is time-consuming, putting together a _____ is worthwhile because
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Answer:
<em>The most he can pay for each of the remaining ladders if he is to obtain a 48% markup goal is </em><em>$36.357</em><em>.</em>
Explanation:
- <em>A hardware buyer plans to purchase 75 ladders which will retail for $35 each. </em>This means that he is going to sell each ladder for $35, regardless of how much he paid for them before.
- <em>He has already placed an order for 48 ladders at $16.50 each</em>. So out of the 75 ladders he is planning to purchase and then sell, he bought 48 at a reduced price of only $16.50 each. Now if we subtract those numbers, as shown below, we determine that he still needs to buy 27 more ladders at an unknown price:
<em>(75 - 48) ladders = 27 ladders</em>
- <em>What is the most he can pay for each of the remaining ladders if he is to obtain a 48% markup goal? </em>So we need to determine the maximum price for each of the remaining 27 ladders if he is to obtain a 48% markup goal.
<em>Markup </em><em>in this case is just a measure of the ratio (in %) between the profit made </em>(by selling 75 ladders for $35 each)<em> to the cost paid </em>(by buying 48 of them at $16.5 each and 27 of them at an unknown price). Its formula is as follows:
Now, we already have our markup goal of 48%, so we can substitute that number into the formula, and divide both sides of the equation by 100:
We know that Cost is the sum of what he paid for the 48 ladders, <em>plus </em>what he is to pay for the remaining 27 ladders, so it should look something like this:
Where '<em>x</em>' is the maximum price he can pay for each of the remaining 27 ladders if he is to obtain a 48% markup goal.
We should also know that Profit is what he gets by selling the 75 ladders, <em>minus </em>the cost paid for them. It should look something like this:
Next, we want to substitute what we have so far for Cost and Profit into the worked Markup formula we had written before, and solve the equation by isolating our '<em>x</em>'. To do that, let's follow these steps:
At this point, <em>we want to transfer the 'x' terms to one side of the equation, and the other terms to the other side</em>, so we get to the answer:
Finally, we divide both sides of the equation by 39.96 ladders:
So the most he can pay for each of the remaining ladders if he is to obtain a 48% markup goal is $36.357. That means that even if he buys the remaining ladders for a higher price than what he is willing to sell them for, he still obtains a 48% markup goal.