Dumping and other material handling operations near a landfill may result in contaminated particles being emitted into the surrounding air. To estimate such particulate emission, the following empirical formula* can be used:

where E is the emission factor (pounds of particles released into the air per ton of soil moved), V is the mean speed of the wind (mph), M is the moisture content of the material (given as a percentage), and k is a constant that depends on the size of the particles.

a. For a small particle (diameter 5 mm), it turns out that k = 0.2. Find E(10, 13).

b. The emission factor E can be multiplied by the number of tons of material handled to obtain a measure of total emissions. Suppose 19 tons of the material in part (a) is handled. How many tons of a second kind of material with k = 0.48 (diameter 15 mm) and moisture content 27% must be handled to achieve the same level of total emissions if the wind velocity stays the same?

c. Sketch several level curves of E(V, M), assuming the size of the particle stays fixed. What is represented by these curves?

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1.3. -1.4 M E(V, M) = k(0.0032)( 32) (1) (+) ¹ 5 2