Question

# Constrained Optimization: Multiple Internal Constraints Fisher Company produces two types of components for airplanes: A and...

Constrained Optimization: Multiple Internal Constraints

Fisher Company produces two types of components for airplanes: A and B, with unit contribution margins of \$400 and \$600, respectively. The components pass through three sequential processes: cutting, welding, and assembly. Data pertaining to these processes and market demand are given below (weekly data).

 Resource Resource Available Resource Usage (A) Resource Usage (B) Cutting 300 machine hours Six hours Ten hours Welding 308 welding hours Ten hours Six hours Assembly 400 labor hours Four hours Ten hours Market demand (A) 50 One unit Zero units Market demand (B) 40 Zero units One unit

Required:

1. Express Fisher Company's constrained optimization problem as a linear programming model. If an an answer box does not require an entry, enter "0" for your answer.

Objective function: Max Z = \$400 A + \$600 B

 Internal constraints: A +  B ≤ (cutting) A +  B ≤ (welding) A +  B ≤ (assembly) External constraints: A ≤ B ≤ Nonnegativity constraints: A ≥ B ≥

2. Select the graph that solves the linear programming model expressed in Requirement 1.

 a. b. c. d.

Which constraints are binding?

3. What if Fisher Company had 10 additional machine hours (cutting) with all other resources held constant? What is the new optimal mix? Enter the appropriate corner point for your answer.

What is the associated total contribution margin? Round the units of A and B to two decimal places, and round intermediate calculations and your final answer to the nearest dollar.

\$

What is the incremental benefit per machine hour caused by the additional ten hours, if any?

\$ per machine hour

 Internal constraints: 6 A + 10 B ≤ 300 (cutting) 10 A + 6 B ≤ 308 (welding) 4 A + 10 B ≤ 400 (assembly) External constraints: A ≤ 50 B ≤ 40 Nonnegativity constraints: A ≥ 0 B ≥ 0 Cutting and Wielding constraints are binding
3. F (point F)

Associated total contribution margin

Units of A = 19.06 units

Units of B = 19.56 units

Associated total contribution margin = 19.06*400 + 19.56*600 = \$19,360

Incremental benefit = 19360-earlier contribution margin = 19360-18800 = \$560.

Incremental benefit per machine hour = 560/10 = \$56 per hour

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