ABCD Ltd is a sports equipment manufacturer that owns and op

ABCD, Ltd. is a sports equipment manufacturer that owns and operates a number of manufacturing plants across the country. The company operates one particular plan where both footballs and basketballs are manufactured. While the company has some flexibility to move manufacturing effort between basketball and football production, the current processes do impose limits on the minimum and maximum number of each ball that can be produced.

Production capacity, cost of materials, labour costs, manufacturing time, and other known constraints are provided below:

Production Capability and Constraints (All unit costs are in $ and time in hours)

Total Machine hours available: Min 39,000 – Max 40,000 hrs.

The number of basketballs that can be produced: Min 30,000 – Max 60,000

The number of footballs that can be produced: Min 20,000 – Max 40,000

Time to manufacture a Basketball: 0.5 hrs.

Time to manufacture a Football: 0.3 hrs.

Cost of labour -- 1 machine hour: $6.00

Cost of material-- 1 Basketball: $2.00

Cost of material-- 1 Football: $1.25

ABCD believes it can sell each basketball for $14.00 and each football for $11.00. Further, the company believes that cost of material and labour costs will not change over the next production cycle.   The corporate tax rate is 28%.

The company wants to determine the ideal number of basketballs and footballs to manufacture that will maximize the facility’s net profit after taxes.

Management Report

Prepare a written management report that includes, at a minimum, the following sections:

Purpose of the Report

Description of the Problem

Methodology (which would include the model formulation)

Findings or Results

Recommendations or Conclusions

Be sure to address all relevant points, discuss any assumptions you are making, and highlight the following items in your report:

A recommendation for the number of basketballs and footballs to manufacture that maximizes net profit after taxes given the existing constraints.

A discussion of which constraints are binding and the amount of slack or surplus in the remaining constraints.

A list of recommendations as to what actions the company may take in the future to increase profitability, and how much extra profit the company might expect if the action is taken. Note that these values can be used by the company to determine whether the expected gain in net profit will offset any capital investment required to implement your recommendations.

Remember that you are writing the report from the point of view of a consultant with senior management of ABCD, Ltd. as the intended audience.

Hints

You need to assume, or guess, an initial number of production units for each product and proceed with using Excel to calculate your Net Revenue for manufacturing. It is ideal to set up a separate section on your spreadsheet that presents the information to be used in the analysis. This information should be organized under the headings “Changing Cells,” “Constants,” “Calculations,” and “Income Statement.”

Once your spreadsheet model is designed, you can proceed with setting Excel SOLVER to carry the calculation. Excel SOLVER is an add-in for MS Excel that can be used for optimization and other linear programming models. Appendix 7.1 on page of 298 of your textbook provides an overview of how to formulate a model and use Solver to extract the required information.

Please also note that your tax will be applied to your Net profit [TR – TC], and if your total cost [TC] is greater than your total revenue [TR], you will have a loss that will be exempted from tax. So, in calculating your Tax you need to use an “IF Statement”, i.e., IF (profit <=0, then put Tax=0, otherwise calculate Tax).

Solution

Let the ideal number of basketballs be x1 and footballs be x2 to manufacture.

Time to manufacture a Basketball: 0.5 hrs. and Cost of material for 1 Basketball: $2.00 and Cost of labor -- 1 machine hour: $6.00

Thus to manufacture x1 Basketball required cost

= (x1)(0.5)(2)(6)=6(x1)………………(1)

Time to manufacture a Football: 0.3 hrs.

Cost of material-- 1 Football: $1.25

Cost of labor -- 1 machine hour: $6.00

Thus to manufacture x2 Football required cost

= (x2)(0.3)(1.25)(6)=22.5(x2) ………………..(2)

So total cost of manufacturing (1)+(2)

That is z=6(x1)+(22.5)x2.

Total Machine hours required for and x2 Football =0.5x1+0.3x2

Total Machine hours available: Min 39,000 – Max 40,000 hrs.

Thus 39000<=0.5x1+0.3x2<=40000

The number of basketballs that can be produced: Min 30,000 – Max 60,000

So 30000<=x1<=60000

The number of footballs that can be produced: Min 20,000 – Max 40,000

20000<=x2<=40000

Thus our problem is to

Minimize       z=6(x1)+(22.5)x2

Subject to

39000<=0.5x1+0.3x2<=40000

30000<=x1<=60000

20000<=x2<=40000

The solution is given by

Global optimal solution found.

Objective value:                              735000.0

Infeasibilities:                              0.000000

Total solver iterations:                             0

Elapsed runtime seconds:                          0.18

Model Class:                                        LP

Total variables:                      2

Nonlinear variables:                  0

Integer variables:                    0

Total constraints:                    7

Nonlinear constraints:                0

Total nonzeros:                      10

Nonlinear nonzeros:                   0

                                Variable           Value        Reduced Cost

                                      X1        60000.00            0.000000

                                      X2        30000.00            0.000000

ABCD believes it can sell each basketball for $14.00 and each football for $11.00.

So 60000 basketballs sale cost=60000*14.00=840000 and each 30000 football sale cost =30000*11.00=$330000.

TR=Total Revenue=840000+330000=$1170000.00

TC=Actual Manufacturing cost =735000.00

Profit =TR-TC=$ 1170000.00-$735000.00=$435000.00

Tax on profit = 435000.00*0.28=$121800.00

So finally Profit – Tax =$435000.00-$121800.00=$313,200.00