Question: The Flair Furniture Company (FFC) manufactures inexpensive wooden tables and chairs. Each table requires 4 hours of carpentry, 2 hours of painting, 30 minutes of inspection time, and 32 linear feet of lumber; each chair requires 3 hours of carpentry, 1 hour of painting, 45 minutes of inspection time, and 10 linear feet of lumber. Each day, 240,100, and 36 hours are available in FFC's carpentry, painting, and inspection departments, respectively. FFC's daily supply of lumber is 1,316 linear feet. Completed tables yield a profit of $7 each, and chairs yield a profit of $5 each. FFC's marketing department believes that there is a limited demand for tables and suggests producing no more than 40 per day. FFC's Operations Research department runs the AMPL script shown below to determine a daily production plan that maximizes profit.

var T >= 0; # Number of tables to produce

var C >= 0; # Number of chairs to produce

maximize profit: 7*T + 5*C;

subject to carpentry: 4*T + 3*C <= 240;

subject to painting: 2*T + C <= 100;

subject to inspection: T/2 + 3*C/4 <= 36;

subject to lumber: 32*T + 10*C <= 1316;

subject to demand: T <= 40;

option solver cplex;

option cplex_options ’sensitivity’;

solve:

display T, C, profit;

display T.down, T.current, T.up;

display C.down, C.current, C.up;

display carpentry.down, carpentry.current, carpentry.up, carpentry.dual;

display painting.down, painting.current, painting.up, painting.dual;

display inspection.down, inspection.current,inspection.up,inspection.dua1;

T = 33 T.down = 3.33333 C.down = 2.1875

C = 26 T.current = 7 C.current = 5

profit = 361 T.up = 16 C.up = 10.5

carpentry.down = 210 painting.down = 92

carpentry.current = 240 painting.current = 100

carpentry.up = 1e+20 painting.up = 1e+20

carpentry.dual = O painting.dual = O

inspection.down = 22.7 lumber.down = 480

inspection.current = 36 lumber.current = 1316

inspection.up = 46.1786 lumber.up = 1468

inspection.dual = 4.73684 lumber.dual = 0.144737

Answer the following questions using the output from the AMPL script shown above. Consider the questions independently and explain your answers.

1. How many tables and chairs should FFC produce daily? What is the profit generated
   from this solution?
2. How many tables and chairs should FFC produce daily if FFC’S sales department decreases the price for chairs by $2 to match a. competitor’s price? What would the optimal daily profit be in this scenario?
3. Which resources (carpentry, painting, and inspection time, and lumber) are currently
   limiting FCC’S daily profit from tables and chairs?
4. Should PFC purchase more lumber if it is available at $0.07 per linear foot?
5. FFC’s owner has been approached by a friend whose company would like to use several hours in the painting department each day. Should FFC sell time to the other company? If so, how much?

Price: $2.99

Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document