Question
(1) Hanson Company has forecast a demand of 10,000 units per month. Which product(s) should Hanson...
(1) Hanson Company has forecast a demand of 10,000 units per month. Which product(s) should Hanson manufacture 10,000 units of to maximize its profits?
(2)Assume that skilled technicians are in short supply so that the total labor hours each month is restricted to 24,000 hrs. How many units of each type should Hanson manufacture (assuming it can sell all it can manufacture)?
(3)Assume that the company can hire any number of skilled technicians, but the machine hrs. are limited to 24,000 hrs. per month. How many of each units should Hanson manufacture (assuming it can sell all it can manufacture)?
(4)Assume that both resources are limited, so that the capacities of each of machine hrs. and labor hrs. are restricted to 24,000 hrs. per month. Now, how many units of each type should Hanson manufacture (assuming it can sell all it can manufacture)?
Making with constrains: The Hanson company sells its products in 3 versions – Regular, premium and luxury. The prices at which one unit of each product can be sold in the market are given by: Product Regular Premium Luxury Market price $550 $600 $680 All three products have to pass through two stages of processing. The manufacturing starts in the company's high tech automated processing plant, and completed by skilled technicians hired by the company. The time required to produce one unit of each of the products is: Product Regular Premium Luxury Machine hours in the processing plant 10 hrs 6 hrs 3 hrs Labor hours of skilled technicians 4 hrs 6 hrs 10 hrs Running the processing plant costs the company $20 per hour, while the skilled technicians charge $50 per hour. The fixed cost of operating the plant for a month is $400,000. Each of the questions below is independent of each other. So please answer each one separately.
Answers
Answer (1) Calculation of Contribution from each product
Particulars Regular Premium Luxury Sales Price (A) 550 600 680 Less- Variable Cost Processing Plant Costs ($20 per hour) 200 120 60 Skilled Technicians Costs ($50 per hour) 200 300 500 Total Variable Costs (B) 400 420 560 Contribution per unit (C) = (A) - (B) 150 180 120 Ranking (II) (I) (III) Since, Premium version will give maximum contribution per unit, All 10,000 units of Premium version is prodused first.
Answer (2) Product ranking as per skilled technician hours is limited
Particulars Regular Premium Luxury Contribution per unit (A) 150 180 120 Skilled technician hour per unit 4 6 10 Contribution per unit per Skilled technician hour 37.5 30 12 Ranking (I) (II) (III) Since, Skilled technician hours are constraint factor, Hanson company will produce that version which gives maximum Contribution per unit per Skilled technician hour i.e. Regular Product.
Total Skilled labour hour = 24,000
Total Units of Regular version be produced = 24000/4 = 6000 units.
Answer 3) Product ranking as per Machine Processing hours is limited
Particulars Regular Premium Luxury Contribution per unit (A) 150 180 120 Machine Processing hour per unit 10 6 3 Contribution per unit per Machine Processing hour 15 30 40 Ranking (III) (II) (I) Since, Machine Processing hours are constraint factor, Hanson company will produce that version which gives maximum Contribution per unit per Machine Processing hour i.e. Luxury Product.
TotalMachine Processing hour = 24,000
Total Units of lUXURY version be produced = 24000/3 = 8000 units.
Answer 4) Product ranking if both Machine Processing hours and Skilled Labour hour is limited-
Product Machine Processing hours is limited Skilled techician hour is limited Maximum Permissible Units Hours/Unit Total Hours Unit Hours/Unit Total Hours Unit Regular 10 24,000 2,400 4 24,000 6,000 2,400 Premium 6 24,000 4,000 6 24,000 4,000 4,000 Luxury 3 24,000 8,000 10 24,000 2,400 2,400 Calculation of Contribution based of maximum permissible units
Particulars Regular Premium Luxury Maximum Permissible units (A) 2400 4000 2400 Contribution per unit (B) 150 180 120 per Machine Processing hour (C) = (A) * (B) 3,60,000 7,20,000 2,88,000 Since, Both Machine Processing hours and skilled technician hours are constraint factor, Hanson company will produce that version which gives maximum Contribution i.e. Premium Product. Whole capcity will be utilised in production of Premium product.
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