Respuesta :
Answer:
Z_max = 30x1 + 100x2
x1 + x2 ≤ 7
4x1 + 10x2 ≤ 40
x1 ≥ 3
x1 ≥ 0
x2 ≥ 0
Step-by-step explanation:
We are told that;
x1 = number of acres of corn planted
x2 = number of acres of wheat planted
We are told that an acre of wheat yields 25 bushels of wheat.
Also that a wheat is sold at $4 a bushel.
Thus, revenue gotten from number of acres of wheat planted = 4 × 25x2 = $100x2
Similarly, for corn;
We are told that an acre of corn yields 10 bushels of corn. Also that corn is sold at $3 a bushel.
Thus, revenue gotten from number of corn planted = 3 × 10x1 = $30x1
Therefore, the objective function will be written as;
Z_max = 30x1 + 100x2
The first constraint we are given is that 7 acres of land are available. Thus;
x1 + x2 ≤ 7
Second constraint is that 40 hours per week of labor are available, Thus;
4x1 + 10x2 ≤ 40
The third constraint is that Government regulations requite that at least 30 bushels of corn be produced during the current year. Thus;
10x1 ≥ 30
This gives; x1 ≥ 3
Now, the number of acres of corn and wheat each planted can't be negative. Thus;
x1 ≥ 0
x2 ≥ 0
