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Carpenter's pricing (Posted on 2018-02-05) Difficulty: 2 of 5
I've found out that our carpenters consider two parameters when asked to quote a customized table's price: the cost is composed of 2 parts. One part is proportional to the area and the other to the square of the larger length.

Then he adds 15% profit and 17% VAT, rounding up to the next integer value divisible by 50.
If the price of 1.2m by 1.8m is  ₪2000 and 1m*3.75m is  ₪5600 what is the price for 2.4m*2.6m dimensions?

Name the price, no discounts, no haggling!

Rem: ₪ stands for NIS, New Israeli Shekel (1$ about 3.5 ₪.)

No Solution Yet Submitted by Ady TZIDON    
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Solution 4 systems solution | Comment 1 of 5
The price before rounding a table of dimensions a by b with a<b can be written as (abx+b^2y)*1.15*1.17=(ax+by)*b*1.15*1.17
where x and y are the parameters

The first table comes out to between 1950 and 2000 which means 
1.2x+1.8y is in the interval (805.15,825.80)
For the second table to come out between 5550 and 5600
1x+3.75y is in the interval (1099.96,1109.87)

To find the parameters there are four extreme scenarios:
LL: both tables came out at the low end of their interval
LH: the first table is at the low end, the second at the high end
HL: the first table came out at the high end, the second at the low
HH: both tables are at the high end

The new table will be priced at (2.4x+2.6y)*2.6*1.15*1.17

Solving each system and finding the price before rounding
LL: x=384.96, y=190.67, price=4966.30
LH: x=378.35, y=195.07, price=4950.89
HL: x=413.64, y=183.02, price=5137.54
HH: x=407.03, y=187.42, price=5122.13

So we see rounded prices anywhere from 5000 to 5150

The range in prices is due to the size of this table.  A small table might have only one possible price.

  Posted by Jer on 2018-02-05 10:09:15
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