Question

Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher’s model. The firm has 900 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 100 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table:

Production Time (hours)
	Cutting		Packaging
Model	and Sewing	Finishing	and Shipping	Profit/Glove
Regular model	1	1/2	1/8	$5
Catcher's model	3/2	1/3	1/4	$8

Assume that the company is interested in maximizing the total profit contribution.

Let R = number of units of regular model.
      C = number of units of catcher’s model.

Max	5  R	+	8  C
s.t.
	1  R	+	3/2  C	≤	900	Cutting and sewing
	1/2  R	+	1/3 C	≤	300	Finishing
	1/8  R	+	1/4  C	≤	100	Packaging and Shipping
			R, C	≥	0

It should have: (or least how to do it)

User Interface.

VBA Code to link Model and Interface

VBA Code for Formatting

VBA Code for Error Trapping

Thank you!

Answer 1

Information Supplied in Question:-

(1) The company is manufacturing two types of gloves :- (a) Regular (b) Catcher

(2) Total time available for cutting and sewing operation:- 900 Hrs

(3) Total time available for the finishing department:- 300 Hrs

(4) Total time available in the packing and shipping department:-100 Hrs

Production Time data of the Company

Model of Gloves Cutting and sewing   Finishing Packing and shipping Profit

Regular 1 1/2 1/8 $5

Catcher 3/2 1/3 1/4 $ 8

What we have to find out:-  

We have to find out linear programming as to maximize the Firm's profit with the help Decision variable, Objectivity function, and Constraints.

Decision Variable:-

These are physical quantities which are controlled by decision-makers. Here the no of two models to be manufactured during the available time is the decision variables.

R = No of Units of Regular model that the firm should manufacture to maximize the profit

C = No of units of catcher's model that the firm should manufacture to maximize the profit

Objective Function :-

Objective function defines the criteria for evaluating the desired parameter. Here we have to find out the profit.

let X = Profit earned per Regular gloves

Y =Profit earned per Catcher gloves

Then the objective function can be written as :

Z = X R + Y C

From the given data table it is clear that X = $ 5 and Y = $ 8

Therefore the profit Function can be written as Z= 5 R + 8 C

Now let us come to the constrains

Constraints:-

These are equalities and inequalities of physical quantities which represent the manufacturing process.

The total available time for cutting and swing is 900 hrs.

From the supplied data it is clear that cutting and sewing for one regular glove is 1 hr and for catcher gloves, it is 3/2 hrs. R and C are the total no of gloves of regular and catcher model.

Total hrs consumed in the manufacture of regular gloves is 1*R and Total hrs consumed in the manufacture of catcher gloves is 3/2*C. And sum of these two can not exceed 900 Hrs

Therefore we can write ; (A) R + 3/2C is always less than or Equal to 900 I,e R + 3/2 C 900

Similarly for Finishing : (B) 1/2 R + 1/3 C is always less than or equal to 300; 1/2 R + 1/3 C 300

And For Packing (C) 1/8 R + 1/4 C is always less than equal to 100; 1/8 R + 1/4 C 100

and shipping

Also, Rand C are no of units manufactured, therefore they can not be negative

(C) R, C is always greater than or equal to Zero R, C    0

Now we can find out the values of R and C from above inequalities

R + 3/2 C = 900

1/2 R + 1/3C =300

We get the values R= 360 AND C=360

• Profit (Max) = 5 R+ 8C = 5* 360 + 8* 360 = 4680 $