A chemical plant makes three major products on a weekly basis. Each of these products requires a certain quantity of raw chemical and different production times, and yields different profits. The pertinent information is given in Table 1. Note that there is sufficient warehouse space at the plant to store a total of 450kg/week.

	Product I	Product II	Product III	Resource Availability
Raw Chemical	7kg	5kg	5kg	3000kg
Production Time	0.05h/kg	0.1h/kg	0.2h/kg	55h/week
Profit	$30/kg	$30/kg	$35/kg

Table I: Datasheet of the three major products of the company

Set up a linear programming problem to maximize profit and solve the linear programming problem with the simplex method manually, as well as by using: i. MATLAB ii. MAPLE iii. Wolfram Mathematica (alongside comments). Compare the results found in the codes written. Also write an algorithm for the same.