Firstly, set up the problem with all details by hand and then you can use Python for solution. Use Python Jupitor Notebook, You should conclude each problem with clear interpretation of the result that you found through your computational work.

A Linear Programming Problem (Problem of minimizing or maximizing a linear objective function)

Consider the following problem of Fiber Optics:

Fiber Optics produces both a low- density and a high-density fiber optic cable. The company has just received a one-time order for 2000 feet of the low-density cable and 4500 feet of the high-density cable for the following week. Each foot of the low-density cable costs $4 to produce and require half a minute of machine time. Each foot of the high-density cable costs $6 to produce and require three-fourths of a minute on the same machine. Because only 40 hours of machine time available next week, Fiber Optics can not meet these demands. However, the company can make up the difference by buying some amount of these cables from a Japanese company at a cost of $7 per foot for the low-density cable and $8 per foot for the high-density cable. You have been asked to find a production/purchase plan for the company that minimizes the cost of meeting the demand while not exceeding the available machine time.

Hint: You need to do following first.

1. Identify the variables

(Use LP and HP for the number of feet of low-density and high-density respectively, cable to produce, and LJ and HJ for the number of feet of low-density and high-density respectively, cable to purchase)

2. Identify the objective function

3. Identify the constraints