Each basketball produced results in a profit of $12, and each football earns $16 in profit.  Z = 12x1 + 16x2where...

Each basketball produced results in a profit of $12, and each football earns $16 in profit. 

Z = 12x₁ + 16x₂ where Z = profit, so maximize Z subject to the following assumptions

Let x₁ = the number of basketballs to produce, x₂ = the number of footballs to produce.

Rubber constraint equation:  3x₁ + 4x₂ ≤ 500 lbs.; Leather constraint equation: 2x₁ + 5x₂ ≤ 800 ft.²

Transforming this model into standard form:

Max Z = 12x₁ + 16x₂

3x₁ + 4x₂ + s₁ = 500

2x₁ + 5x₂ + s₂ = 800

x₁, x₂, s₁, s₂ ≥ 0