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#332401 Coin Triplets
Posted by BMAD on 20 May 2013  10:49 PM
#332388 How Low can U go?
Posted by BMAD on 20 May 2013  07:19 PM
suppose there is a three digit number M where 100*a + 10*b +1*c = M where a, b, and c are digits
What is the minimum value that can be found from M/(a+b+c)?
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#332387 At the Snack Shack
Posted by BMAD on 20 May 2013  07:14 PM
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#332386 A swimmer loses their cap.
Posted by BMAD on 20 May 2013  07:09 PM
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#332384 Ridiculous Inverse
Posted by BMAD on 20 May 2013  07:04 PM
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#332378 An ungrateful award
Posted by BMAD on 20 May 2013  04:36 PM
King Chester awarded a triangular piece of land to his favorite court jester. The three sides measured 150 2/3 yards, 195 3/4 yards, and 45 yards 3 inches. His wife had long been asking him to have a piece of land where she could build a home, a garden, and a temple in each corner. The jester told his wife the good news but was surprised that shew as unhappy. Can you tell why she was unhappy?
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#332377 Breaking through the circle
Posted by BMAD on 20 May 2013  04:18 PM
Prem was doing his homework. With a radius of 20cm he drew a circle. He then drew 7 lines inside the circle with the help of a footrule. Can you tell in how many minimum and maximum divisions was the circle divided by these lines?
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#332367 PowerCo
Posted by BMAD on 20 May 2013  05:21 AM
PowerCo has three plants that must provide enough electricity to four cities. Shipping to each city from the various plants costs varying amounts. Moreover each plant has a set supply of energy that it can send to the various cities. The specifics of this information are outlined in the chart below:
From City 1 City 2 city 3 city 4 Supply
Plant 1 $8 $6 $10 $9 35
Plant 2 $9 $12 $13 $7 50
Plant 3 $14 $9 $16 $5 40
Demand 45 20 30 30
How can PowerCo best minimize its costs?
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#332339 What time is it?
Posted by BMAD on 19 May 2013  02:28 AM
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#332338 Tessellated Pictures
Posted by BMAD on 19 May 2013  02:24 AM
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#332337 Two special numbers
Posted by BMAD on 19 May 2013  02:22 AM
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#332316 Winoc Sells
Posted by BMAD on 17 May 2013  11:55 PM
Winoc sells four types of products. The resources needed to produce one unit of each and the sales prices is listed below:
Resource Product 1 Product 2 Product 3 Product 4
Raw Material 2 3 4 7
Hours of labor 3 4 5 6
Sales Price ($) 4 6 7 8
Currently, 4,600 units of raw material and 5,000 labor hours are available.To meet customer demands, exactly 950 total units must be produced. Customers also demand that at least 400 units of product 4 be produced. What is the solution that maximizes Winoc's sales revenue?
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#332280 The Best Performer
Posted by BMAD on 17 May 2013  04:32 AM
Let a, b, c, and d stand for the fraction of a project that A, B, C, and D can do within each day, respectively.
Spoiler for
It is straightforward to construct a linear equation
Bx = y
where B is a 4x4 matrix given from the OP, and y = (1,1,1,1)'. Solving for x, we get the following values for A, B, C, and D, respectively.
[1,] 0.02614608
[2,] 0.03372183
[3,] 0.04013209
[4,] 0.01705517
Units are project/day. From here, it is simple to compute how much each individual contributes to a project.
I like your answer. It is interesting how in America this problem is solved differently from my home country.
I'm intrigued. How do people from your country solve this problem?
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#332260 Whether to produce desks, tables, or chairs
Posted by BMAD on 17 May 2013  02:49 AM
Resource Desk Table Chair Availability
Lumber 8 board ft 6 board ft 1 board ft 48 board ft
Finishing 4 hours 2 hours 1.5 hours 20 hours
Carpentry 2 hours 1.5 hours 0.5 hours 8 hours
Selling Price $60 $30 $20
Given the constraints listed in terms of time and wood available, how many of each object should be produced to maximize revenue?
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#332256 SteelCo
Posted by BMAD on 17 May 2013  02:38 AM
Steelco has received an order for 100 tons of steel. The order must contain at least 3.5 tons of nickel, at most 3 tons of carbon, and exactly 4 tons of manganese. Steelco receives $20/ton for the order. To fill the order, Steelco can combine four alloys, whose chemical composition and cost is given in the table below:
Alloy (%)
Content 1 2 3 4
Nickel 6 3 2 1
Carbon 3 2 5 6
Manganese 8 3 2 1
Cost/Ton ($) 12 10 8 6
Steelco wants to optimize profit (revenuecosts) obtained from filling the order. How much of each Alloy content type must they produce to achieve optimal profit?
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