Question

Formulate and solve the following problems graphically and by using simplex methods. 2. A store wants to liquidate 200 of its shirts and 100 pairs of pants from last season. They have decided to put together two offers, A and B. Offer A is a package of one shirt and a pair of pants which will sell for $30. Offer B is a package of three shirts and a pair of pants, which will sell for $50. The store does not want to sell less than 20 packages of Offer A and less than 10 of Offer B. How many packages of each do they have to sell to maximize the money generated from the promotion?​

Answer 1

It is an example of linear programming.

It has the following steps:

Explanation:

1. Make a table, determine the variables, write constraints and find the objective function.

2. Represent the feasible region and find its vertices

3. Calculate the value of the function in each vertex and determine the optimum solution

Let x the number of dresses and y the pairs of trousers.

 

The objective function (profit) is

P(x,y) = 40x + 50y

Solving the systems of this pair of equations, we obtain the vertices of the feasible region: (0,0), (0,16), (16,0) and (12,8). Then:

P(0,0) = 0

P(0,16) = 800

P(16,0) = 640

P(12,8) = 880

 

12 dresses and 8 pairs of trousers should be made and the maximum profit is 880 €