Q8 A firm makes product x and y and has a total production of capacity of 9 tones per day x and y requiring the same production capacity. The firm has a permanent contract to supply at least 2 tons of x and at least 3 tones of y per day to another company. Each tonne of x requires 20 machine hours production time and each tonne of y requires 50 machine hours production time, the daily maximum possible number of machine hours is 360. All the firms output can be sold, and the profit made is Rs. 80 per tonne of x and Rs. 120 per tonne of y. It is required to determine the production schedule for maximum profit and to calculate the profit.
Ans: Maximize (Z) = 80×1+120×2
Subject to constraints
x1+x2≤ 9, x1≥2, x2≥3, 20×1+50×2≤360
Non Negative Restrictions x1, x2≥0
Z=960, x1=3, x2=6
