**Problem 1.**

Using graphing strategy plot the graph of the function f(x) =2x^{3} +3x^{2} -12x

**Problem 2:**

The daily demand equations for the sale of brand A coffee and brand B coffee in a supermarket are

Q_{1}(P_{1}, P_{2}) = 200 - 5P_{1} + 4P_{2} (Brand A)

Q_{2}(P_{1}, P_{2}) = 300 + 2P_{1} - 4P_{2} (Brand B),

determine whether the indicated products are competitive, complementary, or neither.

**Problem 3.**

A demand function is given by Q(P)=800-25P

a) Find the elasticity.

b) Find the elasticity at a price of $12 per barrel, stating whether the demand is elastic or inelastic.

c) Find the elasticity at a price of $16 per barrel, stating whether the demand is elastic or inelastic.

d) Find the elasticity at a price of $20 per barrel, stating whether the demand is elastic or inelastic.

**Problem 4.**

Consider Cobb-Douglas production functionQ=9K^{(2/3)}L^{(1/3)}

a) Find total output when K=1000 and L=125.

b) Derive marginal productivity of capital.

c) Derive marginal productivity of labor.

d) Calculate these partial derivatives when K=1000 and L=125

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