1) A manufacturer produces fasteners for the aircraft industry. For each order o

Question

1) A manufacturer produces fasteners for the aircraft industry. For each order of fasters, it costs $3500 to set up the lathe and $1500 for the grinder and $1050 for the automatic packaging machine. An order’s share of a supervisor’s salary is $575. A fastener is processed by a lathe, grinder, and automatic packing machine. A machinist who operates the lathe has hourly compensation is $80 and 80 fasteners are formed per hour. Each grinder operator’s compensation is $60 per hour and 80 fasters can be processed by the grinder per hour. A packager can process 80 fasteners per hour and has compensation $40 per hour. Materials cost $5 per fastener. Suppose x denotes the number of cases produced and sold. Find the following. Suppose a customer is charged $17.50 per fastener.

a) A linear equation which calculates the cost of producing x fasteners.

b) A linear equation which calculates the revenue realized from the sale of x fasteners.

c) A linear equation which calculates the profit realized from the sale of X fasteners.

d) What is the profit or loss realized from the sale of 750 fasteners?

e) What is the break-even point for this product?

f) Suppose a long time customer wants a discount on in order of 875 fasteners. What is the minimum cost the company must charge to breakeven on an order of 875 fasteners?

g) Suppose a new lathe is purchased which can form 160 fasteners per hour and that the grinder and packaging machine can be set to keep up with the improved lathe productivity. What is the break -even point given this improvement?

h) Suppose the company wants to give the lathe operator is an increase of $6 per hour, the grinder operators a raise of $4 and Packers a raise of $3 as an incentive to maintain increased productivity. How many fasteners must be sold to breakeven under these conditions? Assume the changes in part G.

i) Given the information in part H how many fasteners must be produced and sold to realize a profit of $7500?

2) The plant and problem 1 offers compressors for $1000 each for orders up to and including 200 compressors and discounts of $4 times the number of compressors ordered over 200. What order quantity maximizes the manufacturer’s revenue?

Explanation / Answer

a)

Fixed cost per order=cost of lathe+Cost of grinder+ cost of automatic packaging +order’s share of a supervisor’s salary
=3500+1500+1050+575
Variable cost=
Cost of A machinist who operates the lathe+ cost of grinder operator’s compensation +A packager cost+ Materials cost
=X+0.75X+0.5X+5X
so the equation is
7.25X+6625

b)
TR=Price * Quantity
=17.50*X=17.5X
c)
Profit=TR-TC=17.5X-7.25X-6625
=10.25x-6625
D)
Profit=10.25x-6625
=10.25*750-6625
=1062.5
E)
Break even point is at quantity 646
0=10.25x-6625
x=6625/10.25=646.341463

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.