Determine the optimal production quantities

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Reference no: EM132201450

[Based on Albright & Winston (2017)] Western Chassis produces four products: high-quality polished steel sheeting, aluminum sheeting, and two lines of industrial chassis (Standard and Deluxe) for the rack mounting of Internet routers, modems, and other telecommunications equipment. The contribution margin (contribution toward profit) for steel sheeting is $0.40 per pound and for aluminum sheeting is $0.60 per pound. Western earns $12 contribution on the sale of a Standard chassis rack and $15 contribution on a Deluxe chassis rack. During the next production cycle, Western can buy and use up to 25,800 pounds of raw unfinished steel either in sheeting or in chassis. Similarly, 20,400 pounds of aluminum are available for use in sheeting or in chassis. One Standard chassis rack requires 16 pounds of steel and 8 pounds of aluminum. A Deluxe chassis rack requires 12 pounds of each metal. The output of metal sheeting is restricted only by the capacity of the polisher and the availability of raw unfinished steel or aluminum. For the next production cycle, the polisher can handle any mix of the two metals up to 4,000 pounds of metal sheeting. In addition to the availability of raw unfinished steel or aluminum, the Chassis manufacturing can be restricted by either metal stamping or assembly operations; no polishing is required for the manufacturing of Chassis. During the cycle, no more than 2,500 total chassis can be stamped, and there will be 920 hours of assembly time available. The assembly time required is 24 minutes for the Standard chassis rack and 36 minutes for the Deluxe chassis rack. Finally, market conditions limit the number of Standard chassis racks sold to no more than 1,200 Standard and no more than 1,000 Deluxe. Any quantities of metal sheeting can be sold. The plant manger of Western Chassis wants to determine the optimal production quantity for each product for the next production cycle to maximize the total profit. (That is, she wants to determine: pounds of steel sheeting to be produced and sold, pounds of aluminum sheeting to be produced and sold, number of Standard chassis to be produced and sold, and number of Deluxe chassis to be produced and sold.)

Create and solve a Linear Programming (LP) model using Excel Solver ®and determine the optimal production quantities that maximize the total profit. (Apply the color-coding convention used in the book to differentiate between the input cells, decision variable cells and the objective cell.) How many units of each product must the company produce? What is the optimal value of total profit?

Perform sensitivity analysis: Perform a two-way sensitivity analysis using SolverTable ® on the optimal value of the total profit by letting the number of assembly time available vary from 900 hours to 950 hours in increments of 10 hours and the market restriction for the number of Deluxe chassis to be sold vary from 950 units to 1050 units in increments of 10 units. Comment on your findings.

Reference no: EM132201450

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