Please revisit the Max. problem in Chapter 2.(BELOW AFTER THE QUESTION/PROBLEM)

The company is still producing two types of products: bowl and mug. Each bowl needs to have 2 hours of labor, and 4 pounds of clay, which can earn 100 dollars per unit. For each mug, it needs to have 3 hours of labor, and 1 pounds of clay, which can earn 20 dollars per unit. The total number of available labor is 60 hours, and the total number of available clay is 80 pounds.

Please use EXCEL SOLVER to find the optimal solutions and the optimal value of the objective function. That is,

(a) What is the optimal number of bowls to produce?

(b) What is the optimal number of mugs to produce?

(c) What is the optimal value of the objective function?

Chapter 2 Max Problem LP Model Formulation

A Maximization Example

Decision: How many bowls and mugs should be produced to maximize profits given labor and materials constraints?

6LP Model Formulation A Maximization Example Decision: How many bowls and mugs should be produced to maximize profits given labor and materials constraints?

Objective Function and Constraints

Resource Availability:

Decision Variables

Objective Function Resource Constraints

Any Other Constraints?

Whole LP Model

Maximize Z = $70x1+ $20x2

subject to: 1x1+ 2x2 40 4x1+ 3x2 120 x1, x2 0

Feasible Solutions:T/F

x1 = 5 bowls, x2 = 10 mugs B.x1 = 6bowls, x2 = 3mugs C.x1 = 10bowls, x2 = 8mugs

Feasible Solutions are not unique!

Slack Variables& LP Standard Form Standard form requires that all constraints be in the form of equations (equalities)

A slack variable

Be added to a constraint (weak inequality) to convert it to an equation (=)

Typically represents an unused resource

Contributes nothing to the objective function value.

Linear Programming Model: Standard Form

Max Z = 70x1+ 20x2+ 0s1+ 0s2

subject to: 1x1+ 2x2 + s1 = 40 4x1+ 3x2 + s2 = 120x1, x2, s1, s20

Where: x1= number of bowls x2= number of mugs s1, s2 are slack variables