Short answers for sensitivity analysis of Linear Programming:

Blue Ridge wanted to produce the Aqua-Spa and Hydro-Lux, but they only had 200 pumps. The company needed to decide how many of each

 

product to produce to maximize profit. Now suppose Blue Ridge can order additional pumps from a

 

third party for the production. You will need to determine how much to pay for the pumps and

 

additional labor. You will also need to consider how to incorporate a new product line.

             

                                                    Final              Shadow         Constraint        Allowable              Allowable  
                   Name                       Value               Price             R.H. Side           Increase                 Decrease

1. 1  Pumps Req'd Used    200               200                          200                          7                              26

2. Labor Req'd Used         1566               16.6666667           1566                      234                       126

       3.  Tubing Reg'd Used       2712                    0                         2880                  1E+30                      168   

Questions

Q1: Suppose Blue Ridge can order additional pumps from a third party for the production, what is maximum rate that Blue Ridge like to pay for each additional pump?

Q2: If Blue Ridge decides to purchase 10 pumps, what impact will this have on total profit and the optimal solution?

Q3: How much (at most) would you like to pay for 2 more pumps?

Q4: How much (at most) would you like to pay for 100 labor hours?

Q5: How much (at most) would you like to pay for 2 more pumps and 100 labor hours together?

Q6: Suppose a new Hot Tub (the Typhoon-Lagoon) is being considered. It generates a marginal profit of $320 and requires:

1 pump (shadow price = $200)
8 hours of labor (shadow price = $16.67)

13 feet of tubing (shadow price = $0) 

Would it be profitable to produce any?

Q7: Suppose a Typhoon-Lagoon required only 7 labor hours rather than 8. Is it now profitable to produce any? Q8: What is the maximum amount of labor Typhoon-Lagoons could require and still be profitable?

case 2.1 details 

Products: Aqua-Spa and the Hydro-Lux

• They have only 200 pumps available for the next production cycle.

  • Each Aqua-Spa requires 9hrs of labor and 12ft of tubing.

  • Each Hydro-Lux requires 6hrs of labor and 16ft of tubing.

• ○  Blue Ridge expects to have 1566 production labor hours and 2880 ft of tubing during the next production cycle.

• ○  Marginal profit:

  • Aqua-Spa $350

  • Hydro-Lux $300

  • 
    

  •                     AQUA-SPA                 HYDRO-LUX    AVAILABILITY
    

    UNIT PROFIT	$350	$300
    PUMPS	1	1	200
    LABOR	9HRS	6HRS	1566
    TUBING	12FT	16Ft	2880

1X1 + 1X2 ≤ 200 } pumps 9X1 + 6X2 ≤ 1566 } labor 12X1 + 16X2 ≤ 2880 } tubing

X1 ≥ 0 | X2 ≥ 0

THE LP MODEL

MAX: 350X1 + 300X2

Subject to:
1X1+1X2 ≤200}pumps

 9X1+6X2 ≤1566}labor 

12X1+16X2 ≤2880}tubing

X1 ≥ 0
X2 ≥ 0