Question

!!!PLEASE PROVIDE GRAPHS!!! 1. Suppose a small company is in the business of making golf bags...

1. Suppose a small company is in the business of making golf bags to be sold at a local golf course where state championships are often held. They make 2 types of golf bags, a standard bag and a deluxe bag. The table below gives the information for limitations of materials and labor hours, and also for the profit for each type of bag. The materials and labor hours are the amount available per week, and the profit is the profit per week as well.

 Units are per bag Standard Leather (square feet) Premium Leather (square feet) Cutting and Sewing Labor hours Finishing Labor Hours Profit Standard 7 1 3 1 25 Deluxe 0 9 4 2 65 Total available 210 180 120 40

a. From the LP set up derived in HW 3, move your objective function in the direction of maximization on the graph to find the optimal solution. CIRCLE THE OPTIMAL SOLUTION ON THE GRAPH.

b. What are the binding constraints? Why are they binding?

c. Solve the binding constraints for the values of S and D to determine the optimal solution.

d. What is the value of the objective function at the optimal solution?

(a) Let S be the number of standard bags and D be the number of Deluxe bags, then

the formulation of the problem is:

Subject to the constraints

The graph for the optimal solution is:

(b) The constraints are binding as these are restrictions on the availability of resources.

(c) The equations are:

Subject to the constraints

Solving the above constraints we get the feasible points as

O (0, 0), A(30, 0), B(30, 5) and C(0, 20).

(d) So, the value of objective functio at optimal points

 Points Objective Function Z O (0, 0) 0 A (30, 0) 750 B (30, 5) 1075 C (0, 20) 1300 (Optimal Solution)

So, (0, 20) is optimal solution and the value of objective function is 1300 (Unit not known).

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