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.

1. formulate a linear programing model