A product may be made using machine I or machine II. The Manufacturer estimates

Question

A product may be made using machine I or machine II. The Manufacturer estimates that the monthly fixed costs using machine I are $18,000 whereas the monthly fixed costs of using machine II are $15,000. The variable costs of manufacturing 1 unit of product using machine I and machine II are $15 and $20 respectively. The product sells for $50 each.

i) Find the cost functions associated with using each machine.

ii) Which machine should management choose to maximize their profit if the projected sales are $450 units? 550 units? and 650 units?

iii)What is the actual profit or loss for each case in part ii?

I will rate!

Explanation / Answer

i) Let x be the number of machines sold. For machine 1, C1(x)=18000+15x For machine 2, C2(x)=15000+20x
ii)When x=450 C1(450)=24750 C2(450)=24000 So use machine 1 When x=550 C1(550)=26250 C2(550)=26000 So use machine 1 When x=650 C1(650)=27750 C2(650)=28000 So use machine 2 iii) When x=450 and the product sell 50 each(so you earn $22500 of sales) The benefit is: B1(450)=22500-24750= -2250 (loss) B2(450)=22500-24000= -1500 (loss)
When x=550 and the product sell 50 each(so you earn $27500 of sales) The benefit is: B1(550)=27500-26250= 1250 (gain) B2(550)=27500-26000= 1500 (gain) When x=650 and the product sell 50 each(so you earn $32500 of sales) The benefit is: B1(650)=32500-27750= 4750 (gain) B2(650)=32500-28000= 4500 (gain) When x=550 C1(550)=26250 C2(550)=26000 So use machine 1 When x=650 C1(650)=27750 C2(650)=28000 So use machine 2 iii) When x=450 and the product sell 50 each(so you earn $22500 of sales) The benefit is: B1(450)=22500-24750= -2250 (loss) B2(450)=22500-24000= -1500 (loss)
When x=550 and the product sell 50 each(so you earn $27500 of sales) The benefit is: B1(550)=27500-26250= 1250 (gain) B2(550)=27500-26000= 1500 (gain) When x=650 and the product sell 50 each(so you earn $32500 of sales) The benefit is: B1(650)=32500-27750= 4750 (gain) B2(650)=32500-28000= 4500 (gain) C1(550)=26250 C2(550)=26000 So use machine 1 When x=650 C1(650)=27750 C2(650)=28000 So use machine 2 iii) When x=450 and the product sell 50 each(so you earn $22500 of sales) The benefit is: B1(450)=22500-24750= -2250 (loss) B2(450)=22500-24000= -1500 (loss)
When x=550 and the product sell 50 each(so you earn $27500 of sales) The benefit is: B1(550)=27500-26250= 1250 (gain) B2(550)=27500-26000= 1500 (gain) When x=650 and the product sell 50 each(so you earn $32500 of sales) The benefit is: B1(650)=32500-27750= 4750 (gain) B2(650)=32500-28000= 4500 (gain) When x=650 C1(650)=27750 C2(650)=28000 So use machine 2 iii) When x=450 and the product sell 50 each(so you earn $22500 of sales) The benefit is: B1(450)=22500-24750= -2250 (loss) B2(450)=22500-24000= -1500 (loss)
C1(650)=27750 C2(650)=28000 So use machine 2 iii) When x=450 and the product sell 50 each(so you earn $22500 of sales) The benefit is: B1(450)=22500-24750= -2250 (loss) B2(450)=22500-24000= -1500 (loss)
When x=550 and the product sell 50 each(so you earn $27500 of sales) The benefit is: B1(550)=27500-26250= 1250 (gain) B2(550)=27500-26000= 1500 (gain) The benefit is: B1(550)=27500-26250= 1250 (gain) When x=650 and the product sell 50 each(so you earn $32500 of sales) The benefit is: B1(650)=32500-27750= 4750 (gain) B2(650)=32500-28000= 4500 (gain) When x=650 and the product sell 50 each(so you earn $32500 of sales) The benefit is: B1(650)=32500-27750= 4750 (gain) B2(650)=32500-28000= 4500 (gain) The benefit is: B1(650)=32500-27750= 4750 (gain)

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