Best Seats Produces Two Types Of Electric Golf Cart Seats

Best Seats produces two types of electric golf cart seats: a six-seat version and a ten-seat version.

The company has received a large order for 30,000 six-seaters and 15,000 ten-seaters. The production infrastructure consists of three departments: Production, Assembly, and Packaging. The hours of processing time available and the processing time required for each department for both types of seats are provided in the table below: hours available and hours required per unit for each department and seat type. The company makes its in-house six-seaters for $55 and ten-seaters for $85. Alternatively, a new vendor can supply unbranded seats at $67 and $95 respectively. The goal is to determine the number of six and ten-seaters to produce in-house and to buy from the vendor to meet the order at the minimum cost.

Paper For Above instruction

This problem involves formulating and solving a linear programming model to minimize procurement and production costs while meeting large order requirements, constrained by processing capacities across departments.

Formulation of the Model

Let:

  • x1 = number of six-seaters produced in-house
  • x2 = number of ten-seaters produced in-house
  • y1 = number of six-seaters bought from the vendor
  • y2 = number of ten-seaters bought from the vendor

The objective function aims to minimize total costs:

Minimize Z = 55x1 + 85x2 + 67y1 + 95y2

Subject to constraints:

  • Order fulfillment constraints:
  • x1 + y1 ≥ 30,000
  • x2 + y2 ≥ 15,000
  • Capacity constraints based on processing hours in each department (assuming data for hours required and available are provided):

Non-negativity constraints:

  • x1, x2, y1, y2 ≥ 0

Spreadsheet Model and Solution

Using spreadsheet software like Excel, set up a table with decision variables, costs, and constraints. Use Solver to minimize total cost by changing decision variables under the constraints described. The solver is configured with the objective function cell, decision variable cells, and the constraints specified above.

Optimal Solution

The optimal solution determines the quantities of in-house manufacturing and purchasing for each seat type, minimizing total costs while satisfying large order and capacity constraints. The exact solution values depend on the processing time data and are obtained through solver optimization.

References

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