2024 – MA86 Problem Linear Programming Pools and Things Ltd Pools and Things Ltd PATL currently manufactures

 

MA86 Problem: Linear Programming

 

– Pools and Things Ltd.

Pools and Things Ltd. (PATL) currently manufactures swimming pools and pool-related accessories.Recently, a new division, incorporated as a wholly-owned subsidiary, was established under the name of Outdoor Furniture Ltd. (OFL). OFL will produce two types of lawn chairs, regular and lounge.OFL consists of two departments, each requiring specialized equipment and labour skills. Both types of chairs will require processing in each department. The necessary equipment has been purchased and thelabour is being hired. Machine time and labour time will not be interchangeable between the twodepartments. Annual machine and labour time constraints for each department are as follows:

 Machine Hours Labour Hours

Department 1 40,000 25,000Department 2 35,000 20,000Both the regular and lounge chairs are expected to have life cycles of five years with maximum annualsales demands of 32,000 regular chairs and 20,700 lounge chairs. Other available information for thesechairs is as follows:

 Regular LoungeChairs Chairs

Selling price per unit $42 $79Direct materials per unit $5 $8Other variable production costs per unit(including labor and overhead) $20 $41Variable selling costs $2 $3Fixed production costs – allocated 50% to each product (excluding depreciation) $70,000 $70,000Fixed administration costs per year – allocated 50% toeach product (excluding bank loan interest) $130,000 $130,000Machine time per unit:Department 1 1/2hour 1 hour Department 2 1/2hour 1 hour Direct labor time per unit:Department 1 1/2 hour 1/2 hour Department 2 1/4 hour 1/2 hou

 

The beginning balance sheet of OFL consists of the following:- Cash in the amount of $100,000.- New production equipment costing $1,500,000 (straight-line depreciation, expected salvage value of $300,000 at the end of 5 years).- Term loan from the bank in the amount of $1,200,000, requiring quarterly principal payments of $90,000 plus interest, payable at the rate of 1.75% per quarter.- Common shares issued to PATL at a value of $400,000.Additional information is provided in Appendix 1.The controller of PATL, G. Johnson, has arranged an operating line of credit for OFL. The bank’s termsare as follows:1. A maximum of 85% of the projected accounts receivable balance at the end of each quarter will beadvanced by the bank.2. Funds are to be advanced on the first day of a quarter and repaid on the last day of a quarter.Advances and repayments must be in units of $10,000.3. A minimum cash on hand balance of $25,000 must be maintained.4. Interest will be based on an annual rate of 8% and will be payable at the end of each quarter, based onthe quarter’s opening balance.5. OFL must immediately submit to the bank the following information for OFL’s first year of operations: – a cash flow budget for each quarter – a pro-forma income statement for the year – a pro-forma year-end balance sheet.

EXHIBIT 1Information Gathered by BrooksCash Inflows:

– Sales will occur evenly over the year.- 20% of cash from sales will be received in the month of sale, 70% in the following month and 8% inthe third month.- 2% of sales will be uncollectible.

Cash Outflows:

– Variable production and selling costs, excluding direct materials, will be paid in the month of  production.- Direct materials will be received on a just-in-time basis and will be paid 30 days after receipt.- Fixed production and administration costs will be paid evenly throughout the year.- No finished goods inventory will be maintained.- No income tax installment payments will be required during OFL’s first year of operations.

Other Data:

– OFL’s effective tax rate is 40%.- Assets are class 8 at a 20% CCA rate.- OFL uses the percentage of sales basis to estimate bad debts.

 Required –

a. What is the objective function and the constraints in this problem? b. Assume that the linear program provides you with the following optimal solution:Regular Chairs – 30,000Lounge Chairs – 20,000Prepare a cash flow budget for the four quarters of the first year of operations.c. Prepare a budgeted income statement for the first year of operations.d. Prepare a budgeted balance sheet at the end of the first year of operation