Question

Using the simplex method, find the optimal solution to the following LP: A company manufactures three products, A,B, and C. The sales volume for A is at least 50% of the total sales of all three products. However, the company cannot sell more than 75 units of A per day. The three products use one raw material, of which the maximum daily availability is 240 pounds. The usage rates of the raw material are 2 lb per unit of A, 4 lb per unit of B and 3 lb per unit of C. The unit prices of A,B, and C are $20, $50, and $35 respectively.

Answer 1

Let no. of product A be x, Product B be y and product C be z

Total Revenue = 20*x + 50*y + 35*z

We have to maximize this cost

Subject to constraints

x >= 50% (x + y + z)............Constraint for at least 50% of Sales volume

x <= 75................................Company cannot sell more than 75 units of A per day

2x + 4y + 3z <= 240.............Maximum Daily availability of raw material

We solve the given problem in excel using Excel Solver as shown below:

The above solution in the form of formulas along with Excel Solver extract is shown below for better understanding and reference:

As seen from above solution:

No. of Product A = 40 nos

No. of Product B = 40 nos

No. of Product C = 0 nos