A snack food manufacturer buys corn for fortilla chips from two cooperatives, on

Question

A snack food manufacturer buys corn for fortilla chips from two cooperatives, one in Iowa and one in Illinois. The price per unit the Iowa corn is $5.50 and the price per unit of the Illinois corn is $6.00 a. The objective function that represents the total cost can be formulated = TC = 5.5 times 1 = 6 times 2 A constraint equation that the manufacturer needs at least 12000 units of corn can be formulated = x1 + x 2 > = 12000 c. A constraint equation that the Iowa cooperative can supply up 8000 units can be formulated = x1

Explanation / Answer

a) Let x1 and x2 be the number of units of corn bought from Towa and Illinois respectively.

Since, the cost of one unit Towa corn is $5.50, the price of x1 units will be 5.5x1

Similarly, the cost of one unit of Illinois corn is $6, so the price of x2 units will be 6x2

Then the total cost of the corn is the sum of both the costs, that is 5.5x1 + 6x2

We need to minimize the total cost, so the objective function is

Min TC = 5.5x1 + 6x2

b) The number of units of corns bought from both the cooperatives is x1 +x2 and we need at least 1200 of corns that means, the sum of number of corns must be equal to or greater than 12000. So, we get the constraint x1 +x2 .=12000

c) We will constrain equations

x1 +x2 >=12000

x1 <=8000

x2 <=6000

Also, x1 >=0, x2 >=0 (since x1 and x2 are the numbers of units of corns, so they can not be negative)

After plotting the equations we find the common reason (feasible reason) and then note down the corner points of the feasible region.

Now, after getting the corner points, we will find the value of TC using the values of x1 and x2 in objective function The point (x1, x2) where the cost function TC has minimum value will be the optimal solution.

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