1. Supply Function of a good is: P = 3Q + 10 , and it's demand function is: P = 50 - Q2. If the

market is under pure competion , find:

a. Draw Supply and demand function of this good on a graph !

b. Calculate price and quantity at equilibrium condition !

c. Calculate Consumer's Surplus !

d. Calculate price when Producer's Surplus is 10 ! 2. A firm's marginal cost and marginal revenue function are given by: MC = 8 , and MR =

12Q + 4. If fixed costs are 5 , determine :

a. Number of production ( Q ) to achieve Break Even Point !

b. Total Profit if Q = 20 unit !

c. Maximum profit ( if any ). Please explain ! 3. The demand and supply functions of three ( 3 ) interdependent goods are given by:

Qd3 = 17 + P1 + 5P2 - 3P3 Qs3 = 4P3 - 1

Qd2 = 22 + 7P1 - 2P2 + 5P3 Qs2 = 12P2 - 5

Qd1 = 50 - 2P1 + 5P2 - 3P3 Qs1 = 8P1 - 5

Use Cramer's Rule to find the equilibrium prices and quantities of the above

interdependent goods ! 4. Last week chain of caf sold: 1200 cups of coffee , 1400 glasses of apple juice, 1600

glasses of mango juice and 1300 glasses of orange juice. The selling price of coffee: $ 2.50 /

cup; apple juice : $ 1.90/glass; mango juice : $ 1.80/glass ; orange juice: $1.60 /glass .

Production cost of coffee: $1.50/glass; apple juice: $1.20/glass; mango juice: $1.10/glass

and orange juice: $ 1.00/glass. If fixed cost of the caf is neglected, calculate the total

profit last week by using matrix concept ! 7. A furniture company produces table and chair. The production process of those products

require carpentry work and finishing work. Each table takes 4 hours of carpentry work and 2

hours of finishing work. And each chair requires 3 hours of carpentry work and 1 hour of

finishing work. During current production period, 250 hours of carpentry time are available ,

and 110 hours of finishing time are available.

If profit of each table is $100, and profit of each chair is $90 :

a. Formulate the problem as linear programming.

b. Sketch the feasible region and indicate its corner points.

c. If the company wants to reach maximum profit , determine the best possible combination

d. n of tables and chairs to be produced and calculate its maximum profit ! 8. A produce grower is purchasing fertilizer containing three ( 3 ) nutritions: A, B and C. The

minimum needs are: 180 units of A , 220 units of B, and 100 units of C. There are two ( 2 ) popular

brands of fertilizer in the market. "Fast Grow" , costing $ 16 a bag, contains 3 units of A, 5 units

of B, and 1 unit of C. "Easy Grow", costing $ 12 a bag , contains 2 units of each nutrient.

If the grower wishes to minimize cost while still maintaining the nutrients required, how many

bags of each brand should be bought ? can you help me solve these questions step by step I