Q$1.$ A manufacturing company has discontinued the production of a certain unprofitable

product line that led to excess production capacity. Hence the management planned to utilize

this excess capacity for one or more products P$1,$ P$2,$ P$3.$ The available capacity on the various

types and number of machine hours required of associated machinery is listed below:

The sales team indicates that the sales potential for products P$1,$ P$2$ exceeds the maximum

production rate and the sales potential for P$3$ is $20$ units$/$week$.$ The unit profit would be

USD $50,20$ and $25$ respectively on P$1,$ P$2,$ P$3.$ The objective is to determine how much of

each product the company should produce to maximize the profit.

a$.$ Formulate the linear programming model

b$.$ Use python API to solve the model

c$.$ Solve the problem using simplex method, illustrating all the steps in the jupyter

notebook.

d$.$ Verify the solution by generating the results of $($c$)$ using python APIs $4+4+8+4=20M$