A snack food manufacturer buys corn for tortilla chips from two cooperatives, one in Iowa and one in Illinois. The price per unit of the Iowa corn is $6.00 and the price per unit of the Illinois corn is $5.50.

a. Define variables that would tell how many units to purchase from each source.

b. Develop an objective function that would minimize the total cost.

c. The manufacturer needs at least 12,000 units of corn. The Iowa cooperative can supply up to 8000 units, and the Illinois cooperative can supply at least 6000 units. Develop constraints for these conditions.

a. x1 = No. of units to purchase from Iowa

   x2 = No. of units to purchase from Illinois

b. Min 6x1 + 5.5x2

c. x1 + x2 ≥ 12000

   x1 ≤ 8000

   x2 ≥ 6000

Step-by-step explanation:

a. We can consider the variables x1 and x2 as:

x1 = No. of units to purchase from Iowa

x2 = No. of units to purchase from Illinois

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:

Min 6x1 + 5.5x2

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:

x1 + x2 ≥ 12000

x1 ≤ 8000

x2 ≥ 6000

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