Question

A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run. Bagel profits are 20 cents each, and croissant profits are 30 cents each.

1. Which of the following is  not a feasible production combination?

A) 1,100 B and 0 C

B) 0 B and 1,400 C C) 0 B and 0 C D) 0 B and 1.100 C E) 800 B and 600 C

2. What are optimal profits for today's production run?

3. For the production combination of 600 bagels and 800 croissants, which resource is slack (not fully used)?

Answer 1

The LPP is:

Objective Function:

MAX 20*B + 30*C (Here it provides maximum profit in Cents)

Constraints:

Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar.

A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar.

The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run.

We cant use more than what is available:

6*B + 3*C <= 6600 (Constraint 1)

1*B + 1*C <= 1400 (Constraint 2)

2*B + 4*C <= 4800 (Constraint 3)

Question – a:

For 1100 B and 0 C, all constraints are satisfied. Hence this is a feasible point

For 0 B and 1400 C, constraint 3 is not satisfied. Hence this is not a feasible point

For 0 B and 0 C, all constraints are satisfied. Hence this is a feasible point.

For 0 B and 1100 C, All constraints are satisfied. Hence this is a feasible point

For 800 B and 600 C, all constraints are satisfied. Hence this is a feasible point

Answer is: (B)

Question – b:

Optimal Profit:

Putting the LPP in Excel:

A B с D E F G H B с 2 3 4 Objective Function: MAX 20B+30C 0 =20*G2+30*H2 5 6 7 8 RHS LHS 6600 9 Constraints: 6*B+3*C 1*B + 1*C 2*B +4°C Formula (Cell Reference) for LHS 0 =6*G2+3*H2 0 =G2+H2 0=2*G2+4*H2 10 î û î 1400 11 4800 12

Solver Parameters:

х Solver Parameters Set Objective: SES6 H To: Max Min Value Of: 0 By Changing Variable Cells: SG$2:$H$2 2. Subject to the Constraints: ISES9:SES11 <= SDS9:SD$11 Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: GRG Nonlinear Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

Optimal Solution:

А 00 с D E F Н - 1 B с 400 1000 2 3 4 5 6 7 Objective Function: MAX 20B + 30C 38000 =20*G2+30*H2 8 9 <= Constraints: 6*B+3*C 1*B + 1*C 2*B+4*C RHS LHS Formula (Cell Reference) for LHS 6600 5400 =6*G2+3*H2 1400 1400 =G2+H2 4800 4800 =2*G2+4*H2 10 11 12

Hence the optimal profit is: 38000 cents

Question – c:

For B = 600, C = 800;

Constraint Flour is: 6*600 + 3*800 = 3600 + 2400 = 6000. RHS is 6600. Hence this is one slack

Constraint Yeast is: 600 + 800 = 1400. RHS = 1400. This is not a slack

Constraint Sugar is: 2*600 + 4*800 = 1200 + 3200 = 4400. RHS is 4800. Hence this is a slack.

Answer is: Slack resources are: Flour and Sugar

********

IF YOU HAVE ANY DOUBT, KINDLY COMMENT. I WOULD LOVE TO HELP YOU!!!

IF YOU LIKE THE ANSWER, PLEASE GIVE AN UP-VOTE OR THUMB UP. THIS WILL ENCOURAGE ME TO ANSWER MORE!!