A potter is making cups and plates. It takes her 6 minutes to make a cup and 3 minutes to make a plate. Each cup uses 3/4lb. of clay and each plate uses one lb. of clay. She has 20 hours available for making the cups and plates and has 250lbs. of clay on hand. She makes a profit of $2 on each cup and $1.50 on each plate.

What are your constraints?

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The constraints of the problem are the time available and the amount of clay on hand. The potter has 20 hours available for making cups and plates and has 250lbs. of clay on hand. These constraints determine how many cups and plates can be made within the given limitations.

To find the number of cups and plates that can be made, we need to figure out the amount of time and clay required for each cup and plate, and then divide the total time and clay available by those amounts.

First, let's calculate the time and clay required for each cup and plate:

- Time required for a cup: 6 minutes
- Time required for a plate: 3 minutes
- Clay required for a cup: 3/4 lb
- Clay required for a plate: 1 lb

Now we can calculate the maximum number of cups and plates that can be made:

- Maximum number of cups: (Total time available in minutes) / (Time required for a cup)
- Maximum number of plates: (Total time available in minutes) / (Time required for a plate)

To convert the total time available from hours to minutes, we multiply it by 60. So:

- Maximum number of cups: (20 hours * 60 minutes/hour) / 6 minutes
- Maximum number of plates: (20 hours * 60 minutes/hour) / 3 minutes

Next, we need to calculate the maximum number of cups and plates based on the available clay:

- Maximum number of cups: (Total clay available in pounds) / (Clay required for a cup)
- Maximum number of plates: (Total clay available in pounds) / (Clay required for a plate)

Finally, to determine the number of cups and plates that can be made, we take the minimum of the two maximums:

- Number of cups: Minimum(Maximum number of cups based on time, Maximum number of cups based on clay)
- Number of plates: Minimum(Maximum number of plates based on time, Maximum number of plates based on clay)