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in Linear Programming by (15 points)
edited by

A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess. When a student ' A' takes food for 20 days he has to pay Rs 1300 as hostel charges whereas a student 'B', who takes for 25 days, pays Rs 1500 as hostel charges.  Find the fixed charges and the cost of food per day.

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Let Rs. x be monthly fixed charge of hostel & Rs.y be the cost of food per day

For student A, x  + 20 y = 1300---(1)

For student B, x + 25y = 1500----(2)

Substract (1) from (2), we get

(x + 25y) - (x + 20y) = 1500 - 1300

⇒ 5y = 200

⇒ y = 40

∴ x + 800 = 1300 (From (1))

⇒ x = 1300 - 800 = 500

Hence, hostal fixed charge is Rs. 500 and the cost of food Rs. 40 per day

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