Question & Answer: (b) The number of machine hours required for each unit of the respective products…..

The number of machine hours required for each unit of the respective products is shown in the following table. (b) Product 2 Product 3 Machine Type Milling Machine Lathe Grinder Product 1 0 Suppose that the unit costs for producing products 1, 2, and 3 are RM 25, RM 10, and RM 15, respectively, and that the prices required (in RM) in order to be able to sell xi, x2, and X3 units are | 35+100x13·1 15+40x, | . and 20+50x2, respectively. Formulate a nonlinear programming model for the problem of determining how many units of each product the firm should produce to (7 marks) (i) maximize the profit. (ii) Verify that this problem is a convex programming problem (6 marks)

(b) The number of machine hours required for each unit of the respective products is shown in the following table. Suppose that the unit costs for producing products 1, 2, and 3 are RM 25, RM 10, and RM 15, respectively, and that the prices required (in RM) in order to be able to sell x_1, x_2, and x_3 units are (35 + 100x^-1/3_1), (15 + 40x^-1/4_2), and (20 + 50x^-1/2_3), respectively. (i) Formulate a nonlinear programming model for the problem of determining how many units of each product the firm should produce to maximize the profit. (ii) Verify that this problem is a convex programming problem.

Expert Answer

Answer

As there is no limit, it can go as much as it can, so there needs to be additional constrain for the same.

x1 x2 x3
42443371.29 53687091 2122169
Mc Type Prod 1 Prod 2 Prod 3
Milling 9 3 5
Lathe 5 4 0
Grinder 3 0 2
Cost 25 10 15
Price 34917.15366 3438.95 72858.32
Profit 111164.4278
Maximization

This is a sample not the optimal solution. Optimal solution is infinity.

Still stressed from student homework?
Get quality assistance from academic writers!