number of kgs. for each ingredients to use in order to minimize the total cost for 10000 kgs

Question

Bill and Bro’s chemical ltd. must produce 10,000 kgs. of a special mixture for a customer. The
mix consists of ingredients A, B and C. The costs of ingredients are $8 per kg for A, $ 10 per
kg for B and $11 per kg for C. No more than 35,000 kgs of A can be used and at least 1500
kgs of B must be used. Also at least 2000 kgs of C is required. Calculate the number of kgs.
for each ingredients to use in order to minimize the total cost for 10000 kgs.

Answer 1

The hardest part is defining the constraints. You are minimizine the sumproduct of 8*A + 10*B + 11*C. This is your objective function. Set up the excel file with amounts of A,B,C in 3 cells in a column and then the costs as above in the next column. These two columns will define your sumproduct. Now you just have to list the constraints. You are going to minimize the sumproduct by changing the variables in the A B and C amounts columns. Think of your constraints. A, B and C are nonnegative. Also, A <= 35000, B <=10000 and B >= 1500 and C <=10000 and >=2000.  You have one more limiting constraint. Amounts of A + B + C >= 10000. If you correctly enter these and run solver you will get a solution. Note that you could limit this more, i.e. A is really <=10000, or even more limiting, but with the given conditions you get a solution because you are maximizing an output (10000 lbs) and minimizing the cost.