Can you make a linear maximization model for this problem?

Question

The ploughman familiy ows 640 acre farm.Entire familiy can produce 9500 person hour labor a year. If some of tihis is not needed they work nest farm fo $5 hour.Farm support 2 types of livestock; dairy cows and hens as well as 3 crops soybeans corn and wheat(all 3 are cash crops but corn is used for cow feed and wheat used for chicken).succesful harvest for this year is $20000. family has 30 cows valued at $35000 and 2000 hens valued at $5000. each cow require 2 acre land and 10 person hours labor and generates $850 for 1 month. for each hen there is not significant acreage 0,05 person hours labor and 1 hen generates $4,25 for 1 month. for 1 acre ; soybeans requires 2,4 person hours and generates $70 for 1 year. Wheat requires 1,4 person hours and generates $40 a year. corn requires 2,1 person hour labor and generates $60 for a year. they want to maximize their profit from cows, hens, soybeans, corn and wheat

Answer 1

No, unless you presume the revenue generated are net profits.

The only problem with this question relates to the phrase "ll 3 are cash crops but corn is used for cow feed and wheat used for chicken." This implies that some acreage used for food is actually going into the cow and chicken production as an input. Since we cannot know how much is being eaten, we cannot know the true cost of the cows and chickens and the marginal costs in lost grain revenue. It confuses the question of does a cow take 10 hours of labor or 10 hours of labor plus 2.1*number of acres in hours to harvest feed corn?

It could still be done as a maximization problem, but if you did it, you could not use software. Rather, you would substitute the unknown relationships and solve that way using the tableau method, treating unknown variables as numbers.