Write the mathematical formulation for the following problems. Clearly state the variables (eq.x,y,z) and the meaning of the variables used by you in the formulation. Write the objective function and the constraints for the linear programming problem. No Need to find the optimal solutions, just write the formulation. Q1) A clay potter wants to make and sell bowls and plates. A bowl uses 5 pounds of clay. A plate uses 4 pounds of clay. The potter has 40 pounds of clay and wants to make at least 5 bowls. The profit on a bowl is $32 and the profit on a plate is $34. Write a linear programming formulation for the potter to decide how many bowls and how many plates should the potter make to maximize the profit? (Just write the mathematical formulation) (15 Marks) Q2) Trees help keep air fresh by absorbing carbon dioxide. The city of Normal has $2100 to spend on planting spruce and maple trees. The land available for planting is 45,000 square feet. Spruce trees cost $30 to plant and require 600 square feet of space. Maple trees cost $40 to plant and require 900 square feet of space. Spruce trees absorb 650lb/yr of carbon dioxide and maple trees absorb 300lb/yr of carbon dioxide. Write a linear programming formulation to decide how many of each tree should be planted to maximize carbon dioxide absorption? (15 Marks) Q3) A seafood restaurant owner orders at least 50 fishes. He cannot use more than 30 amberjack (fish type 1) or more than 35 flounder (fish type 2). Amberjack costs $4 each and flounder costs $3 each. How many of each fish should he use to minimize his cost? (15 Marks) Q4) Juan makes two types of wood clocks to sell at local stores. It takes him 2 hours to assemble a pine clock, which requires 1 oz of varnish. It takes 2 hours to assemble an oak clock, which takes 4oz. of varnish. Juan has 16oz. of varnish in stock and can work 20 hours. He makes $3 profit on each pine clock and $4 on each oak clock. Write a linear programming formulation which decided how many of each type should he make to maximize his profits? (15 Marks)