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Statistics Help

**Question: **Question : A toy factory produces 150 toys per hour. The workers produce toyss 8 hours a day, 21 days a month at a cost of $250,000 per work month. Overtime production costs $1,750 per hour. If the toys are priced at $15 each, the factory can manage to sell all the toys produced during the 8 hour day. The factory marketer insisted that they can sell an additional 3,000 plushies per month if they lower the price of each toy to $14. The owner noted that this would actually decrease profits.How many dollars would this reduce profit by? Edit

**Answer: **Lets look at costs the place is paying to make the toys when selling at 15 bucks first.

We know that it costs the factory 250000 for a normal work month. That’s 4 weeks of 5 days each equals 20 days. BUT the factory works 21 days a month, or one extra day. We know that each work day is 8 hours and it costs the factory 1750 dollars per each hour.

8X1750=14000 dollars for the extra “overtime day”

Now 250000 per normal work week plus the extra overtime day.

250000 + 14000=264000 dollars to operate the factory for the 21 days that they are making toys. Remember that number 264000 its very important.

Now, lets look at what they can produce in those 21 days of operation.

We know that they make 150 toys per hour and that they work 8 hours each day.

150Toys x 8hours= 1200 toys per day.

1200 toys per day x 21 days of working =25200 toys made in one month. Remember that.

They sell the toys for 15 dollars each and make 25200 per month. So

15 dollars x 25200 toys a month = 378000 dollars of expected income per month. Not bad….

BUT it cost them 264000 dollars to make those toys.

We have to figure the factories profit.

378000 income per month MINUS 264000 dollars it cost to make the toys

378000- 264000= 114000 dollars profit.

This tells us that as the factory is working right now and selling their toys for 15 bucks they can expect to make 114000 dollars profit. This is a key piece of info, remember it.

Now we have to figure out what happens if the factory makes 3000 MORE toys and sells them for less, or 14 dollars each.

so let’s look at how long it will take to make the extra 3000 toys.

looking back at our information provided in the math problem, we are told that the factory can’t produce 150 toys per hour. we know that we have to produce an additional 3000 toys.

3000 toys divided by 150 per hour=20 hours to produce the extra toys.

now that we know how long it will take to produce the extra toys, we have to determine how much it will cost to produce the extra toys.

because we know that the workers are already working overtime, we know that all of the time that it takes to produce the extra toys will also be over time.

again referring to our given information, we are told that it cost 1750 dollars per hour to operate the factory during overtime. we know that it will take 20 hours to produce the extra toys. So

1750 dollars in overtime x 20 hours to make the extra toys = 35000 dollars in overtime expenses to make the extra toys.

NOW

we must keep in mind that it cost the factory 264000 dollars to make the original number of toys and that the extra toys must be added to that. So

264000 dollars to operate the factory as in our first example + 35000 to make the extra toys= 299000 dollars.

It will cost the factory 299,000 dollars to produce the original toys and the extra toys.

to figure a profit in this new example we have to remember that the factory is making 25200 toys on the original example. Now they have added another 3000.

25200 toys + 3000 extra toys= 28200 total toys

they want to sell these toys cheaper, at 14 dollars each. So

14 dollars per toy x 28200= 394800 dollars in sales. BUT…

We need to figure out the profit in this second example. We can do this the same way as we did before.

394800 dollars in sales – 299000 cost= 95800.

The factory can expect a profit of 95800 dollars if they operate as in this second example.

They have made less money than in the first example.

114000 dollars profit from example one

95800 dollars profit in example two

114000 – 95800= 18200 dollars less Edit

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