a) Find an optimal solution to Western's problem. What is the production plan, and what is the total revenue? b) Obtain a sensitivity report for the solution reported in Part (a). Which constraints are binding? c) What is the incremental contribution associated with adding an hour of assembly time? Over what range of increase is the marginal value valid?
Western Chassis produces high-quality polished steel and aluminum sheeting and two lines of industrial chassis 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. 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. For the next production cycle, the polisher can handle any mix of the two metals up to 4,000 pounds of metal sheeting. Chassis manufacture can be restricted by either metal stamping or assembly operations; no polishing is required. 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.
a) Find an optimal solution to Western's problem. What is the production plan, and what is the total revenue?
b) Obtain a sensitivity report for the solution reported in Part (a). Which constraints are binding?
c) What is the incremental contribution associated with adding an hour of assembly time? Over what range of increase is the marginal value valid?
d) What is the value of additional capacity on the polisher? How much increase and decrease in this capacity is possible before a change occurs in the optimal production
e) An advertising agency has devised a marketing plan for the Western Chassis Company that will increase the market for Deluxe chassis. The plan will increase demand by 75 Deluxe chassis per month at a cost of $100 per month. Should Western adopt the plan? Briefly explain why.
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