Answer:
a. <u>x1 = No. of units to purchase from Iowa</u>
<u>x2 = No. of units to purchase from Illinois</u>
<u></u>
b. <u>Min 6x1 + 5.5x2</u>
<u></u>
c. <u>x1 + x2 ≥ 12000</u>
<u>x1 ≤ 8000</u>
<u>x2 ≥ 6000</u>
Step-by-step explanation:
a. We can consider the variables x1 and x2 as:
<u>x1 = No. of units to purchase from Iowa</u>
<u>x2 = No. of units to purchase from Illinois</u>
<u></u>
b. Price per unit of Iowa corn = $6
Price per unit of Illinois corn = $5.5
Objective function that would minimize the total cost can be written as:
<u>Min 6x1 + 5.5x2</u>
<u></u>
c. The manufacturer needs at least 12000 units of corn which means that the combined number of units from Iowa and Illinois must be greater than or equal to 12000. So, we can write:
x1 + x2 ≥ 12000
The Iowa cooperative can supply up to 8000 units which means that the value of x1 must not be greater than 8000. So, we can write:
x1 ≤ 8000
Similarly, the Illinois cooperative can supply at least 6000 units which means that the value of x2 must not be less than 6000. So, we can write:
x2 ≥ 6000.
The constraints for these conditions are:
<u>x1 + x2 ≥ 12000</u>
<u>x1 ≤ 8000</u>
<u>x2 ≥ 6000</u>
