posted by BJ .
Here gasoline output is mesured in thousands of gallons, fiber output in the thousands of square feet, and crude oil in thousands of barrels. The product's profits per unit output are $.50 per gallon for gasoline and $.75 per square foot for fiber. The the respective marginal profits are:
Mg = ($.50)MPg = ($.50)(72 - 3Mg) = 36 - 1.5Mg
Mf = ($.75)MPf = ($.75)(80 - 4Mf) = 60 - 3Mf
Setting these equal to each other and rearranging gives:
Mf = .5Mg + 8.
Solving this equation and constraint Mg + Mf = 20 implies Mg = 8 thousand barrels and Mf = 12 thousand barrels. This allocation generates 480 thousand gallons of gasoline and 672 thousand sq ft of fiber. The firm's total profit is $744 thou.
I have to find the optimal crude oil from the above equation I did. The profit associtated with the fiber if it were cut in half, that is, fell to $.375 per sq ft.
Mf = ($.375)(80 - 4Mf) = 30 - 1.13Mf
Mg = 4 thou
Mf - 16 thou
480 thousand gallons of gasoline
336 square feet of fiber
Would the profit still remain the same?
Please check my math? Thanks