A farm co-op has over 40,500 gallons of fertilizer/herbicide available to use when planting corn and soybeans. The farm co-op's maximum profit for using 40,500 gallons of fertilizer/herbicide is $315,009 and the maximum profit for 40,508 gallons is $315,034. What is the profit value of each additional gallon of fertilizer/herbicide (that is, the shadow price of a gallon of fertilizer/herbicide)? Round your answer to the nearest cent if necessary.
A) $3.57
B) $3.13
C) $2.78
D) $25.00
E) $12.50

Question

A farm co-op has over 40,500 gallons of fertilizer/herbicide available to use when planting corn and soybeans. The farm co-op's maximum profit for using 40,500 gallons of fertilizer/herbicide is $315,009 and the maximum profit for 40,508 gallons is $315,034. What is the profit value of each additional gallon of fertilizer/herbicide (that is, the shadow price of a gallon of fertilizer/herbicide)? Round your answer to the nearest cent if necessary. ​
A) $3.57
B) $3.13
C) $2.78
D) $25.00
E) $12.50

Quizplus · Accepted Answer

To find the shadow price of a gallon of fertilizer/herbicide, we need to calculate the slope of the line connecting the two maximum profit points, which represents the marginal benefit of the additional fertilizer/herbicide.

Marginal benefit = (change in profit) / (change in gallons) = ($315,034 - $315,009) / (40,508 - 40,500) = $25 / 8

Rounding to the nearest cent, the shadow price of a gallon of fertilizer/herbicide is $3.13.

Therefore, the best choice is B.

A Farm Co-Op Has Over 40,500 Gallons of Fertilizer/herbicide Available