A farm supply store carries 50–lb bags of both grain pellets and grain mash for pig feed. It can store 600 bag?
Posted by adminA farm supply store carries 50–lb bags of both grain pellets and grain mash for pig feed. It can store 600 bags of pig feed. At least twice as many of its customers prefer the mash to the pellets. The store buys the pellets for $3.75 per bag and sells them for $6.00. It buys the mash for $2.50 per bag and sells it for $4.00. If the store orders no more than $1,400 worth of pig feed, how many bags of mash should the store order to make the most profit?
The store’s budget for pig feed won’t allow it to buy 600 bags of mash. Since mash costs the store less than pellets, the storage capacity is not a relevant constraint. They can store as much as they can afford to order.
The profit on mash is 60% ($1.50 / $2.50).
The profit on pellets is 60% ($2.25 / $3.75).
The store will therefore make the same profit on its investment, for any amount it sells. They should therefore order to suit their customer demand.
Now we’ve got a problem, in that we’re not given a clear statement of customer demand: “at least twice as many” isn’t specific enough. However, let’s assume that what we want to do is to spend that $1,400 on twice as many bags of mash as of pellets.
Then if x is the number of bags of pellets purchased (half the number of bags of mash), we can see that
2.5 (2x) + 3.75x = 1400
8.75x = 1400
x = 1400 / 8.75 = 160
So the store can purchase 160 bags of pellets ($600) and 320 bags of mash ($800) and expect to realize a 60% profit ($840) if it sells all the pig feed.
May 6th, 2009 at 4:10 am
The store’s budget for pig feed won’t allow it to buy 600 bags of mash. Since mash costs the store less than pellets, the storage capacity is not a relevant constraint. They can store as much as they can afford to order.
The profit on mash is 60% ($1.50 / $2.50).
The profit on pellets is 60% ($2.25 / $3.75).
The store will therefore make the same profit on its investment, for any amount it sells. They should therefore order to suit their customer demand.
Now we’ve got a problem, in that we’re not given a clear statement of customer demand: “at least twice as many” isn’t specific enough. However, let’s assume that what we want to do is to spend that $1,400 on twice as many bags of mash as of pellets.
Then if x is the number of bags of pellets purchased (half the number of bags of mash), we can see that
2.5 (2x) + 3.75x = 1400
8.75x = 1400
x = 1400 / 8.75 = 160
So the store can purchase 160 bags of pellets ($600) and 320 bags of mash ($800) and expect to realize a 60% profit ($840) if it sells all the pig feed.
References :
May 6th, 2009 at 4:16 am
It is reasonable that maximum profits will come when a store provides what the customers want. So, if 2 out of three customers want mash, then it is reasonable that maximum profits will be obtained when the store carries 2 bags of mash for every 1 bag of pellets, or 2/3 of the bags are mash. You did not say if the $1,400 “worth” of feed is at the purchase price or at the selling price. I will assume that it is at the purchase price.
Total cost is the $2.50 purchase price times 2/3 of total BAGS (for mash), plus $3.75 times 1/3 of total BAGS (for pellets). This equals $1,400:
$2.50 x (2/3) x BAGS + $3.75 x (1/3) x Bags = $1,400
This simplifies to
($5.00/3) x BAGS + ($3.75/3) x BAGS = $1,400
Multiplying each side by 3:
3 x ($5.00/3) x BAGS + 3 x ($3.75/3) x BAGS = 3 x $1,400
This simplifies to
$5.00 x BAGS + $3.75 x BAGS = $4,200
Which further simplifies to
$8.75 x BAGS = $4,200
Dividing each side by $8.75 we get
$8.75/$8.75 x BAGS = $4,200/$8.75
BAGS = 480
This is the total number of bags to order. 2/3 of the bags should be mash, so they should order 480 x 2 / 3 = 320 bags of mash.
If the $1,400 “worth” of feed is at the selling price, substitute the selling prices for the purchase prices above and rework the problem.
References :