Scenario

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.

Required

Prepare management report with following sections

Purpose of the Report

Description of the Problem

Methodology (which would include the model formulation)

Findings or Results

Recommendations or Conclusions

Following things must be covered

1. A recommendation for the number of basketballs and footballs to manufacture that maximizes net profit after taxes given the existing constraints.
2. A discussion of which constraints are binding and the amount of slack or surplus in the remaining constraints.
3. 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.

Hints to complete the work

1. 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."
2. Once your spreadsheet model is designed, you can proceed with setting Excel SOLVER to carry the calculation.
3. 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). If you are going to graph something use Desmos.com and it will make your life easier