Joyce Lumber Company Joyce Lumber Company produces tables and chairs. The produc

Question

Joyce Lumber Company Joyce Lumber Company produces tables and chairs. The production process for each is similar in that both require a certain number of labor hours in the carpentry department and a certain number of hours in the painting department. Each table takes three hours of carpentry work and two hours of painting work. Each chair requires four hours of carpentry and one hour of painting. During the current month, 2, 400 hours of carpentry time and 1,000 hours of painting time are available. The marketing department wants the company to make no more than 450 new chairs this month because of an overabundance of available chairs. However, because the existing inventory of tables is low, the marketing, department wants the company to make at least 100 tables this month. Each table sold makes a profit contribution of $7 and each chair sold makes a profit of $5. Joyce Lumber's problem to determine the best possible combination of tables and chairs to manufacture this month in order to attain the maximum profit. The firm would like to solve this as a linear programming problem. Use the information below to answer the following questions. Joyce Lumber Co. a) What is the optimal production solution to this problem? What is the total profit? b) What are the allowable numbers of chairs and tables that can be produced before the optimal solution changes? c) What is the impact on profits of a decrease in painting time of 100 hours? Does the optimal solution change? d) What is the impact on profits of an increase in carpentry time of 200 hours? Does the optimal solution change? e) Will the optimal solution change if the market price is able to increase and the profit per chair increases $4?

Explanation / Answer

a)

The optimal production for the given scenario will happen when 320 tables and 360 chairs are produced. And the total profit under the optimal production is $4040.

b)

The allowable number of chairs is less than 450 and the allowable number of tables is greater than 100.

c)

By solving this case under SOLVER addin in EXCEL we get,

Here we can see that the profit has decreased from $4040 to $3780. Also the number of chairs produced has increased and the number of chairs produced for optimal solution has decreased.

d)

The results for this scenario when there is an increase in the number of carpentry hours by 200 hours is given below.

We can see clearly that the total profit has increases from the optimal solution which is given with the problem. Also the number of chairs produced has increased and the number of tables produced has decreased.

e) In this scenario the optimal solution should not change however ther should be an increase in optimal profit since the profit of chair has been increased. Using SOLVER we get the results for this scenario as,

Variables Tables Chairs # Units 240 420 Profits 7 5 3780 Constraints Carpentry 3 4 2400 <= 2400 Painting 2 1 900 <= 900 Max Chairs 0 1 420 <= 450 Min Table 1 0 240 >= 100

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