Q1. Given the revenue function in Riyal Omani per unit p = -3x2 + 600x and...

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Q1. Given the revenue function in Riyal Omani per unit p = -3x2 + 600x and the average cost function in Riyal Omani C(x) = 30x? + 180x. Find: (4 Marks) (a). The marginal revenue at x = 10 units. (a). The marginal cost at x = 10 units. Q2. (2+3+2=7 Marks) dy (i) If y = (sinx + cosx)secx, then find dx (ii) If y = 3x-2 - then find y". (iii) If f (x) = x?sinx + 2xcosx + 2sinx, then find f'(x). Q3. Find the value of x and y from the following system of linear equations using the Gauss- (4 Marks) Jordan elimination method. x + 3y = 8 y = 9 3x - Q4. Mr. Ali is on a special diet and know that his daily requirement of two nutrients is 80 milligrams of vitamin C, and 60 milligrams of magnesium. He has two supplements to choose from: type A and type B. Type A costs 2 $ per tablet, and type B costs 3$ per tablet. Type A contains 20 milligrams of vitamin C, and 30 milligrams of magnesium. Type B contains 30 milligrams of vitamin C and 25 milligrams of magnesium. How many of each tablet should he take each day to meet his minimum requirements while spending the least amount of money? (Use algebraic method to find the minimum requirements) (5 Marks) Q5. Solve the following linear programming maximization problem using Simplex Tableau (5 Marks) method. z = 4x + 3y Subject to the constraints: x + y< 9 2x + y < 13 x 2 0, y 2 0. Q1. Given the revenue function in Riyal Omani per unit p = -3x2 + 600x and the average cost function in Riyal Omani C(x) = 30x? + 180x. Find: (4 Marks) (a). The marginal revenue at x = 10 units. (a). The marginal cost at x = 10 units. Q2. (2+3+2=7 Marks) dy (i) If y = (sinx + cosx)secx, then find dx (ii) If y = 3x-2 - then find y". (iii) If f (x) = x?sinx + 2xcosx + 2sinx, then find f'(x). Q3. Find the value of x and y from the following system of linear equations using the Gauss- (4 Marks) Jordan elimination method. x + 3y = 8 y = 9 3x - Q4. Mr. Ali is on a special diet and know that his daily requirement of two nutrients is 80 milligrams of vitamin C, and 60 milligrams of magnesium. He has two supplements to choose from: type A and type B. Type A costs 2 $ per tablet, and type B costs 3$ per tablet. Type A contains 20 milligrams of vitamin C, and 30 milligrams of magnesium. Type B contains 30 milligrams of vitamin C and 25 milligrams of magnesium. How many of each tablet should he take each day to meet his minimum requirements while spending the least amount of money? (Use algebraic method to find the minimum requirements) (5 Marks) Q5. Solve the following linear programming maximization problem using Simplex Tableau (5 Marks) method. z = 4x + 3y Subject to the constraints: x + y< 9 2x + y < 13 x 2 0, y 2 0.