[Excel spreadsheet available at http://web.mit.edu/15.053/www/Exer3.1.xls] Outdoors, Inc. has, as…
[Excel spreadsheet available at http://web.mit.edu/15.053/www/Exer3.1.xls] Outdoors, Inc. has, as one of its product lines, lawn furniture. They currently have three items in that line: a lawn chair, a standard bench, and a table. These products are produced in a two-step manufacturing process involving the tube-bending department and the welding department. The time required by each item in each department is as follows:
The contribution that Outdoors, Inc. receives from the manufacture and sale of one unit of each product is $3 for a chair, $3 for a bench, and $5 for a table.
The company is trying to plan its production mix for the current selling season. It feels that it can sell any number it produces, but unfortunately production is further limited by available material, because of a pro longer strike. The company currently has on hand 2000 lbs. of tubing. The three products require the following amounts of this tubing: 2 lbs. per chair, 3 lbs. per bench, and 4.5 lbs. per table. In order to determine the optimal product mix, the production manager has formulated the linear program shown in Fig. and obtained the results shown in Fig.
a) What is the optimal production mix? What contribution can the firm anticipate by producing this mix?
b) What is the value of one unit more of tube-bending time? of welding time? of metal tubing?
c) A local distributor has offered to sell Outdoors, Inc. some additional metal tubing for $0.60/lb. Should Outdoors buy it? If yes, how much would the firm’s contribution increase if they bought 500 lbs. and used it in an optimal fashion?
d) If Outdoors, Inc. feels that it must produce at least 100 benches to round out its product line, what effect will that have on its contribution?
e) The R&D department has been redesigning the bench to make it more profitable. The new design will require 1.1 hours of tube-bending time, 2.0 hours of welding time, and 2.0 lbs. of metal tubing. If it can sell one unit of this bench with a unit contribution of $3, what effect will it have on overall contribution?
f) Marketing has suggested a new patio awning that would require 1.8 hours of tube-bending time, 0.5 hours of welding time, and 1.3 lbs. of metal tubing. What contribution must this new product have to make it attractive to produce this season?
g) Outdoors, Inc. has a chance to sell some of its capacity in tube bending at cost + $1.50/hour. If it sells 200 hours at that price, how will this affect contribution?
h) If the contribution on chairs were to decrease to $2.50, what would be the optimal production mix and what contribution would this production plan give?