Question

In which year is the quantity of PDS supply the minimum ?

• A. 2011
• B. 2012
• C. 2016
• D. 2015

Hint:

When comparing years with percentages, always calculate absolute values (production %) instead of just looking at percentages.

Answer 1

The Correct Option is A

Step 1: Formula for PDS supply PDS supply in a year = (Total production of that year) \(\times\) (PDS %). 

Step 2: Calculate totals from graph 2011: \( 300 + 250 + 150 + 200 = 900 \) thousand tonnes. 
2012: \( 350 + 150 + 50 + 250 = 800 \) thousand tonnes. 
2013: \( 300 + 400 + 200 + 100 = 1000 \) thousand tonnes. 
2014: \( 350 + 100 + 150 + 200 = 800 \) thousand tonnes. 
2015: \( 300 + 150 + 250 + 350 = 1050 \) thousand tonnes. 
2016: \( 400 + 300 + 350 + 250 = 1300 \) thousand tonnes. 

Step 3: Apply PDS % from table 2011: \( 900 \times 12\% = 108 \) (thousand tonnes). 
2012: \( 800 \times 18\% = 144 \). 
2013: \( 1000 \times 16\% = 160 \). 
2014: \( 800 \times 14\% = 112 \). 
2015: \( 1050 \times 20\% = 210 \). 
2016: \( 1300 \times 22\% = 286 \). 

Step 4: Find the minimum Minimum PDS supply = 108 (thousand tonnes) in 2011. \[ \boxed{2011} \]

Answer 2

Instead of computing PDS supply for all six years and comparing at the end, the minimum can be narrowed down early by spotting which years combine a modest production total with the lowest PDS percentages.

Identifying likely candidates. Scanning the PDS percentages, 2011 (12%) and 2014 (14%) are the two lowest, making them the natural candidates for the minimum PDS supply.

Verifying with exact computation. \[ 2011:\ 900\times12\%=108,\qquad 2014:\ 800\times14\%=112. \] Checking the remaining years confirms none come close: \[ 2012:\ 800\times18\%=144,\quad 2013:\ 1000\times16\%=160,\quad 2015:\ 1050\times20\%=210,\quad 2016:\ 1300\times22\%=286. \]

1. Option 2011: Matches — gives the minimum PDS supply of \(108\) thousand tonnes.
2. Option 2012: Its value of \(144\) is well above the minimum; ruled out.
3. Option 2016: Its value of \(286\) is the highest of all six years, not the lowest; ruled out.
4. Option 2015: Its value of \(210\) is also far above the minimum; ruled out.

Narrowing to the two lowest-percentage years first, then verifying exactly, confirms 2011 gives the smallest PDS supply.

So the correct answer is 2011.