(a) Assume the price of product from company A is p and the quantity of product from company A is qA. Due to the supply-demand relationship, p is proportional to -q and can be expressed as p = -kqA + Po. The cost of each product is c. Let y be the profit of company A. How many should company A produce to realize the maximal profit? (5 points) (b) Assume there's also company B in the market. The price of product from company B is also p and the quantity of product from company B is qB. Now the price is determined by the total quantity: p = -K(qA+qB) + po. The cost of each product is also c. Given the quantity of product from company B is x, how many should company A produce to realize the maximal profit? (10 points) (c) If both company A and B want to realize their maximal profit, what is the price of the product would be? (5 points) (a) Assume the price of product from company A is p and the quantity of product from company A is qA. Due to the supply-demand relationship, p is proportional to -q and can be expressed as p = -kqA + Po. The cost of each product is c. Let y be the profit of company A. How many should company A produce to realize the maximal profit? (5 points) (b) Assume there's also company B in the market. The price of product from company B is also p and the quantity of product from company B is qB. Now the price is determined by the total quantity: p = -K(qA+qB) + po. The cost of each product is also c. Given the quantity of product from company B is x, how many should company A produce to realize the maximal profit? (10 points) (c) If both company A and B want to realize their maximal profit, what is the price of the product would be? (5 points)