Optimization and assignment problems

Questions involving discrete optimization scenarios such as worker-task assignment, route planning, or resource allocation using operations research techniques rather than curve analysis.

5 questions · Moderate -0.9

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OCR MEI C4 2013 June Q1
2 marks Easy -2.0
The diagram is a copy of Fig. 4. R is a place with latitude \(45°\) north and longitude \(60°\) west. Show the position of R on the diagram. M is the sub-solar point. It is on the Greenwich meridian and the declination of the sun is \(+20°\). Show the position of M on the diagram. [2] \includegraphics{figure_4}
OCR MEI C4 2013 June Q2
3 marks Easy -1.2
Use Fig. 8 to estimate the difference in the length of daylight between places with latitudes of \(30°\) south and \(60°\) south on the day for which the graph applies. [3]
OCR MEI C4 2013 June Q3
2 marks Easy -1.2
The graph is a copy of Fig. 6. The article says that it shows the terminator in the cases where the sun has declination \(10°\) north, \(1°\) north, \(5°\) south and \(15°\) south. Identify which curve (A, B, C or D) relates to which declination. [2] \includegraphics{figure_6}
\(10°\) north:
\(1°\) north:
\(5°\) south:
\(15°\) south:
OCR MEI C4 2013 June Q4
4 marks Moderate -0.5
In lines 94 and 95 the article says "Fig. 8 shows you that at latitude \(60°\) north the terminator passes approximately through time \(+9\) hours and \(-9\) hours so that there are about 18 hours of daylight." Use Equation (4) to check the accuracy of the figure of 18 hours. [4]
OCR MEI C4 2013 June Q5
7 marks Standard +0.3
  1. Use Equation (3) to calculate the declination of the sun on February 2nd. [3]
  2. The town of Boston, in Lincolnshire, has latitude \(53°\) north and longitude \(0°\). Calculate the time of sunset in Boston on February 2nd. Give your answer in hours and minutes using the 24-hour clock. [4]