i. In the factory, machine 1 makes 8 inch pliers at rate of 60 units per hour and 6 inch pliers at rate of 70 units per hour. Machine 2 makes 8 inch pliers at rate of 40 units per hour and 6 inch pliers at rate of 20 units per hour. It costs $50 per hour to operate machine 1, where as machine 2 costs $30 per hour to operate. Production schedule needs that at least 240 units of 8 inch pliers and at least 140 units of 6 inch pliers should be made during each 10 hour day. Which combination of machines will cost least money to operate?
ii. Perimeter of the rectangle is 24 inches and its area is 35 square inches. Write down its dimensions?
iii. The Broadway theater has 485 seats, divided into main, orchestra and balcony seating. Main seats for $35, balcony seats for $20 and Orchestra seats sell for $50. If all seats are sold, gross revenue to theater is $15550. If all main and balcony seats are sold, but only half orchestra seats are sold, gross revenue is $13300. How many are there of evry type of seat?
iv. Solve equations
25x+61y-12z=25
18x-12y+7z=10
2 x+3 y-z=-3
for x,y,z.
v. Solve system
y=6 x+1
6x^2+y^2=1