Firms often face the problem of allocating an input in fixed

Firms often face the problem of allocating an input in fixed supply among different products. Find the optimal crude oil allocation for the following example if the profit associated with square foot of fiber is cut to $0.375, while the profit associated with per gallon of gasoline stayed at $0.50.

• What is gasoline marginal profit, given gasoline production function of QG = 72MG – 1.5 MG2,

• What is fiber marginal profit, given fiber production function of QF = 80MF – 2MF2,

• Determine the maximize profit.

• Determine total input availability.

Solution

1.

Marginal profit of gasoline is its per-unit profit, $0.50

2.

Marginal profit of fiber is its per-unit profit, $0.140625

Fiber = $0.375

Fiber = 0.140625