hitch balls statistics

You buy tow hitch balls in large lots for the tow tractors you manufacture. You estimate that it costs you approximately 20% of cost to store a ball for a year.

Ordering cost is estimated to be $49 per order and your annual demand is for 5000 balls.

Your supplier offers you the following price schedule:

QUANTITY DISCOUNT (%) DISCOUNT COST
0 to 999 0 $5.00
1000 to 1999 4 $4.80
2000 or more 5 $4.75

The discount cost is for all balls in the order.

You operate 5 days per week, 52 weeks per year, minus 7 paid holidays.
a. What price per ball should you pay to minimize total cost?

b. How many balls should you order at each time?

c. How many orders will you make per year?

d. What is your total cost for balls each year?

9. Slixtrix Conversions, located in Waldo, Florida specializes in conversions of pick-up trucks and vans. In particular, they do a very good business in their signature line of each.

The business has three production shops which, using good project scheduling skills, work on the vehicles simultaneously. The shops are preparation, upholstery, and electric/electronics.

The company nets $5000 for each truck and $6000 for each van produced and sold. The work requirements for each, in hours, and personnel available are given in the table below. Personnel work 8 hours per day, five days per week on the conversions.

shop trucks vans personnel
preparation 8 12 10
upholstery 10 8 8
electrical 12 16 12

The company has standing orders for 12 trucks and 10 vans per week, and is able to obtain parts for only 20 vans per week.
a. How many trucks and vans should they produce each week to maximize profit and remain within the stated bounds?
b. What shops or other constraints determine the optimum solution?
c. Are any shops over staffed? If so which ones? If people from that shop were able to work in another shop would transferring any from that shop improve profitability? (how many, from where, to where?)

13. ABC manufacturing company has orders for three similar castings used in aircraft engine fuel pumps. The company has three N/C machines that can machine the castings at the same production rate. However, because of varying defect / rejection rates, the unit costs of the products vary depending on the machine utilized. The following table gives the capacities by machine and the unit costs, by product, by machine for the parts, and the demand for each type casting.

Develop the minimum cost production schedule for making the required number of parts. (Which machines make which parts?)

Product

Machine A B C

Capacity
1 1.00 1.20 .90 1500
2 1.30 1.40 1.20 1500
3 1.10 1.00 1.20 1500
Demand 2000 500 1200