Question

In: Operations Management

Bibbins Manufacturing produces softballs and baseballs for youth recreation leagues. Each softball sells for $21, while...

Bibbins Manufacturing produces softballs and baseballs for youth recreation leagues. Each softball sells for $21, while each baseball sells for $24. The material and labor required to produce each item is listed here along with the availability of each resource. Formulate and solve the math programming model to determine the mix of products to make which will maximize profit while making sure each product comprises no less than 1/3 of the total unit production. In reading your solution state which of the resources below you have in excess over what is needed for the optimal mix of softballs and baseballs.

Resource

Amount Required For

Amount Available

Cost

Softball

Baseball

Leather

5 oz.

4 oz.

325 lbs.

$6/lb.

Nylon

6 yds.

3 yds.

5,400 yds.

$15/100 yds.

Core

4 oz.

2 oz.

250 lbs.

$9/lb.

General Labor

2.5 min.

2 min.

20 hours

$10/hr.

Stitching Labor

5 min.

4 min.

50 hours

$18/hr.

Solutions

Expert Solution

Decision variables:

Let the number of softballs be x and baseballs be y

Objective function:

Maximize Z= 21x+24y-1.55417(x+y)

Constraints:

5x+4y<=5200 (Leather)

6x+3y<=5400 (Nylon)

4x+2y<=4000 (Core)

2.5x+2y<=1200 (General labour)

5x+4y<=3000 (Stiching Labour)

x>=(x+y)/3 (Minimum production for Softball)

y>=(x+y)/3 (Minimum production for baseball)

x,y>=0 (non-negative)

keosha answered 1 year ago
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