CUSTOMIZING UNITS

A fruit salesman wishes to keep track of his fruit sale and expenses. He deals in a variety of fruits including apples, oranges, strawberries, bananas and peaches. Set up a customized system of units to do so.

Use the definitions of mass, length, time, charge and temperature as pounds, boxes, hours, dollars, and pieces (of fruit) respectively. The individual types of fruit will be defined later.

First, under the Math / Options menu, select 'None' for the unit system and define base unit labels as shown at the right. Realize that doing so will only define unit LABELS. The actual unit will be defined later. NOTE: When typing a base unit definition such as 1T, MathCAD will insert a space between the '1' and the 'T'. Use your arrow key to backup and delete the space.

Next, define each unit in terms of the base unit.

Now define each type of fruit as a 'piece'. This will act as a label only; it will still be seen by MathCAD as a piece.

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NOTE: When doing homework, you do not have to
type in the above expressions. It is provided for lecturing purposes only.

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The selling price of each type of fruit is as follows:
apples: 0.89/lb
orange: 0.69/lb
strawberries: 1.29/lb
bananas: 0.29/lb
peaches: 0.49/lb

On the average, there are 32 apples in a box. A single box of apples has a net weight of approximately 13.5 lbs. What is the price of a box of apples? What is the price per apple? On the average, how many apples comprise a pound? What is the average weight per apple? Assign appropriate units to solve the problem.

A single bunch of bananas costs 1.29 and has approximately 7 bananas. How many bananas (pieces) must sell to bring in the same amount of money as an apple? Define

Since the unit banana and the unit apple is a redefinition of the base unit piece, the value of Y/X is unitless as 'seen' by MathCAD. Note that you can define the unit either way (mathematically); but only one is correct!