lesson business math : pls do in the piece paper with a4 paper Question 4: Given the demand function: ? = 200 − 2? − ?? + 0.1?2 Where P = 10, PA= 15 and Y = 100, find: a. The price elasticity of demand b. The cross-price elasticity of demand; substitute or complementary goods? c. The income elasticity of demand; inferior, normal, or superior goods? Unconstrained Optimization: Profit Maximization Question 5: A firm is a monopolistic producer of two goods G1 and G2. The prices are related to quantities Q1 and Q2 according to the demand functions. ?1 = 50 − ?1 ?2 = 95 − 3?2 If the total cost function is: ?? = ?12 + 3?1?2 + ?22 Find the values of Q1 and Q2 which maximize π and deduce the corresponding prices. Lagrange Multipliers Question 6: Use Lagrange multipliers to find the maximum value of: ? = 4?? Subject to the constraint: ? + 2? = 40 Definite Integration: Investment Flow Question 7: If the investment flow is: ?(?) = 9000√? Calculate: a. The capital formation from the end of the first year to the end of the fourth year; b. The number of years required before the capital stock exceeds $100,000
lesson business math : pls do in the piece paper with a4 paper
Question 4:
Given the demand function:
? = 200 − 2? − ?? + 0.1?2
Where P = 10, PA= 15 and Y = 100, find: a. The
b. The cross-price elasticity of demand; substitute or complementary goods?
c. The income elasticity of demand; inferior, normal, or superior goods?
Unconstrained Optimization: Profit Maximization
Question 5:
A firm is a monopolistic producer of two goods G1 and G2. The prices are related to quantities Q1 and Q2 according to the demand functions.
?1 = 50 − ?1 ?2 = 95 − 3?2
If the total cost function is:
?? = ?12 + 3?1?2 + ?22
Find the values of Q1 and Q2 which maximize π and deduce the corresponding prices.
Lagrange Multipliers
Question 6:
Use Lagrange multipliers to find the maximum value of:
? = 4??
Subject to the constraint:
? + 2? = 40
Definite Integration: Investment Flow
Question 7:
If the investment flow is:
?(?) = 9000√? Calculate:
a. The capital formation from the end of the first year to the end of the fourth year;
b. The number of years required before the capital stock exceeds $100,000.
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