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A Farmer Plans to Plant Two Crops, a and B

Question 196

Multiple Choice

A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre, whereas that of crop B is $60/acre. The farmer has a maximum of $5,400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 2,300 labor-hours available. If she expects to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should she plant in order to maximize her profit? ​
Find the range of values that the contribution to the profit of an acre of crop A can assume without changing the optimal solution.
​
Find the range of values that the resource associated with the constraint on the land available can assume.
​
Find the shadow price for the resource associated with the constraint on the land available.
​


A) Crop A = 15 acres, Crop B = 80 acres A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre, whereas that of crop B is $60/acre. The farmer has a maximum of $5,400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 2,300 labor-hours available. If she expects to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should she plant in order to maximize her profit? ​ Find the range of values that the contribution to the profit of an acre of crop A can assume without changing the optimal solution. ​ Find the range of values that the resource associated with the constraint on the land available can assume. ​ Find the shadow price for the resource associated with the constraint on the land available. ​ A) Crop A = 15 acres, Crop B = 80 acres 1) 25 B) Crop A = 15 acres, Crop B = 80 acres 1) 25 C) Crop A = 80 acres, Crop B = 15 acres 1) 25 ​ D) Crop A = 15 acres, Crop B = 80 acres 1) 25 ​ A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre, whereas that of crop B is $60/acre. The farmer has a maximum of $5,400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 2,300 labor-hours available. If she expects to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should she plant in order to maximize her profit? ​ Find the range of values that the contribution to the profit of an acre of crop A can assume without changing the optimal solution. ​ Find the range of values that the resource associated with the constraint on the land available can assume. ​ Find the shadow price for the resource associated with the constraint on the land available. ​ A) Crop A = 15 acres, Crop B = 80 acres 1) 25 B) Crop A = 15 acres, Crop B = 80 acres 1) 25 C) Crop A = 80 acres, Crop B = 15 acres 1) 25 ​ D) Crop A = 15 acres, Crop B = 80 acres 1) 25 ​
1) 25
B) Crop A = 15 acres, Crop B = 80 acres A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre, whereas that of crop B is $60/acre. The farmer has a maximum of $5,400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 2,300 labor-hours available. If she expects to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should she plant in order to maximize her profit? ​ Find the range of values that the contribution to the profit of an acre of crop A can assume without changing the optimal solution. ​ Find the range of values that the resource associated with the constraint on the land available can assume. ​ Find the shadow price for the resource associated with the constraint on the land available. ​ A) Crop A = 15 acres, Crop B = 80 acres 1) 25 B) Crop A = 15 acres, Crop B = 80 acres 1) 25 C) Crop A = 80 acres, Crop B = 15 acres 1) 25 ​ D) Crop A = 15 acres, Crop B = 80 acres 1) 25 ​ A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre, whereas that of crop B is $60/acre. The farmer has a maximum of $5,400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 2,300 labor-hours available. If she expects to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should she plant in order to maximize her profit? ​ Find the range of values that the contribution to the profit of an acre of crop A can assume without changing the optimal solution. ​ Find the range of values that the resource associated with the constraint on the land available can assume. ​ Find the shadow price for the resource associated with the constraint on the land available. ​ A) Crop A = 15 acres, Crop B = 80 acres 1) 25 B) Crop A = 15 acres, Crop B = 80 acres 1) 25 C) Crop A = 80 acres, Crop B = 15 acres 1) 25 ​ D) Crop A = 15 acres, Crop B = 80 acres 1) 25 ​
1) 25
C) Crop A = 80 acres, Crop B = 15 acres A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre, whereas that of crop B is $60/acre. The farmer has a maximum of $5,400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 2,300 labor-hours available. If she expects to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should she plant in order to maximize her profit? ​ Find the range of values that the contribution to the profit of an acre of crop A can assume without changing the optimal solution. ​ Find the range of values that the resource associated with the constraint on the land available can assume. ​ Find the shadow price for the resource associated with the constraint on the land available. ​ A) Crop A = 15 acres, Crop B = 80 acres 1) 25 B) Crop A = 15 acres, Crop B = 80 acres 1) 25 C) Crop A = 80 acres, Crop B = 15 acres 1) 25 ​ D) Crop A = 15 acres, Crop B = 80 acres 1) 25 ​ A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre, whereas that of crop B is $60/acre. The farmer has a maximum of $5,400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 2,300 labor-hours available. If she expects to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should she plant in order to maximize her profit? ​ Find the range of values that the contribution to the profit of an acre of crop A can assume without changing the optimal solution. ​ Find the range of values that the resource associated with the constraint on the land available can assume. ​ Find the shadow price for the resource associated with the constraint on the land available. ​ A) Crop A = 15 acres, Crop B = 80 acres 1) 25 B) Crop A = 15 acres, Crop B = 80 acres 1) 25 C) Crop A = 80 acres, Crop B = 15 acres 1) 25 ​ D) Crop A = 15 acres, Crop B = 80 acres 1) 25 ​
1) 25
​
D) Crop A = 15 acres, Crop B = 80 acres A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre, whereas that of crop B is $60/acre. The farmer has a maximum of $5,400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 2,300 labor-hours available. If she expects to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should she plant in order to maximize her profit? ​ Find the range of values that the contribution to the profit of an acre of crop A can assume without changing the optimal solution. ​ Find the range of values that the resource associated with the constraint on the land available can assume. ​ Find the shadow price for the resource associated with the constraint on the land available. ​ A) Crop A = 15 acres, Crop B = 80 acres 1) 25 B) Crop A = 15 acres, Crop B = 80 acres 1) 25 C) Crop A = 80 acres, Crop B = 15 acres 1) 25 ​ D) Crop A = 15 acres, Crop B = 80 acres 1) 25 ​ A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre, whereas that of crop B is $60/acre. The farmer has a maximum of $5,400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 2,300 labor-hours available. If she expects to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should she plant in order to maximize her profit? ​ Find the range of values that the contribution to the profit of an acre of crop A can assume without changing the optimal solution. ​ Find the range of values that the resource associated with the constraint on the land available can assume. ​ Find the shadow price for the resource associated with the constraint on the land available. ​ A) Crop A = 15 acres, Crop B = 80 acres 1) 25 B) Crop A = 15 acres, Crop B = 80 acres 1) 25 C) Crop A = 80 acres, Crop B = 15 acres 1) 25 ​ D) Crop A = 15 acres, Crop B = 80 acres 1) 25 ​
1) 25
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