Question

Nigel dreamed that he was an elf. In Santa's factory at the North Pole, he made toy vehicles -- airplanes, boats, and cars -- that Santa delivered to the 20,000 good little boys and girls all around Southern Louisiana. Nigel made these toy vehicles using wire, rubber, and paint.
Each airplane was built with 3 centimeters of wire and 7 grams of rubber. Each boat was built with 8 centimeters of wire and 5 grams of rubber. Each car was built with 4 centimeters of wire and 8 grams of rubber. It took 9 milliliters of paint to paint an airplane, 2 milliliters of paint to paint a boat, and 3 milliliters of paint to paint a car.
It would take 4 airplanes to make one child happy, 3 boats to make one child happy, and 4 cars to make one child happy. Nigel had 20 meters of wire, 70 kilograms of rubber, and 50 liters of paint, and wanted to make toys that would make the greatest possible number of children happy.
Let x be the number of airplanes, y be the number of boats, and z be the number of cars that Nigel makes.

Check all of the following that would be objective functions in this linear programming problem.

A. 9x+2y+3z≤50,000
B. 9x+2y+3z≤50
C. 8x+5y
D. 1/4x+1/3y+1/4z
E. 4x+3y+4z
F. 3x+7y
G. 1/9x+1/2y+1/3z≥50,000
H. 9x+2y+3z
I. z≥0
J. x≤0
K. 4x+8y
L. 4x+3y+4z≥20,000
M. 1/4x+1/3y+1/4z≥20,000
N. 7x+5y+8z≤70,000
O. 7x+5y+8z≤70
P. 1/9x+1/2y+1/3z