PLEASE COMPLETE WITH MATLAB

MATLAB

Now that you know where to dig and how your spiral separator works and performs, you need to work out your method of operation to extract as much gold as you can in 5 hours on the beach. Here are some things that you will need to consider, and which become clearer after watching the spiral separator video:

1. Each dirt load processed by the spiral separator is 3 shovel loads worth.

2. Assume that 3 shovel loads of dirt correspond to a 5 L load in the spiral separator.

3. Assume that each shovel load takes 10 seconds to dig and place in the spiral separator.

4. You need to clean out the tailings bin every time you have processed 15 L of dirt.

5. A clean out of the tailings bin and refilling it with water and reassembling the spiral separator in

   the bin ready for the next round of processing takes 2 minutes.

6. As the video shows, the spiral bowl itself never needs to be cleaned out and you can just keep

   processing after the bin has been cleaned out and the setup reassembled.

In addition, there are a few other assumptions that might be helpful:

7. Assume that the width of your shovel is 20 cm.

8. Assume that the gold concentration at the location that you are digging stays constant

9. Assume that you can move along the beach and stay at the same gold concentration as long as

   your distance from the water line at mid tide stays the same.

10. Assume that the tide does not have any influence on your session as it is falling very slowly from

    the mid tide point and that the change over the five hour session you are undertaking is negligible in the context of what you are doing.

In other words based on points (1 - 10), just assume that you are always digging sand with a constant gold concentration.

A) Write an equation (which may include one or more unknowns) that describes the total gold in grams that you would extract with the spiral separator and digging the sands with the highest gold concentration on this beach, after working for 5 hours. Use fprintf to print comments that explain your workings IN FULL in the command window output.

HINT: Break the problem down into a single cycle of:

1. Digging 3 shovel loads of sand and placing them into the spiral separator.

2. Spinning the spiral separator.

3. Repeating steps 1 & 2 three times.

4. Cleaning out the tailings bin and resetting the spiral separator assembly.

   This cycle (steps 1 4) is then repeated for a total time of 5 hours working on this beach.

B) Determine the optimal spinning time for each load in your spiral separator to maximise the mass of gold extracted after 5 hours of work. Use fprintf to report this spinning time per load (to the nearest second) as well as the recovery (as a fraction < 1 to 3 decimal places) that corresponds to this spinning time.

C) Using the function that you obtained in (Task A), report how much gold you extracted for the 5 hour session in grams (to 3 decimal places) using fprintf.

D) Use fprintf again to report how much you earned in $/hour (to the nearest cent) as a result of the mass of gold you extracted in this 5 hour session, assuming gold to be worth $80/gram. Would you say that this is an attractive job considering the returns?

E) To answer this, use fprintf to give the ratio of your earnings in $/hour to that of your most efficient friend (to 3 significant figures).