Morse Furniture is planning a weekend sale. It has selected tables and chairs as

Question

Morse Furniture is planning a weekend sale. It has selected tables and chairs as the two items for sale. Each table takes up 2.8 square feet of space, will cost the firm $17, and will sell for $26. Each chair takes up 1.7 square foot of space, will cost the firm $9 and will retail for $19. Morse has only 230 square feet of space to display the tables and chairs, and a budget of $2,000 for procuring the tables and chairs. According to demand estimates, the store does not expect to sell more than 90 chairs. Formulate the linear program to decide the number of chairs and tables to stock in order to maximize total profit.

(a) What is the optimal solution to the problem? (b)What is the value of the objective function at the optimal solution? (c)Within what ranges would the objective function coefficients vary without changing the optimal solution? Explain. (d)Interpret the dual (shadow) prices of the constraints. (e)Within what ranges would the right-hand side values vary without changing the interpretation of the dual prices of the constraints? Explain.

Explanation / Answer

Let x be the number of tables and y be the number of chairs to be made.

Profit from each Table = $26 - $17 = $9

Profit from each chair = $19 - $9 = $10

So our objective function will be:

Maximize z = 9x + 10y

The constriants will be:

2.8x + 1.7y < 230

17x + 9y < 2000

y < 90

x, y > 0

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