MAT540 Quantitative Methods Week 8 Assignment Linear Programming Case Study Complete Solution

Question: #1343

Week 8 Assignment

Linear Programming Case Study

A company called SDV Cycle Stopsells adult bicycles, adult mopeds, and attachable child seats. The unit profit (price) for each item is as follows:

	Bicycles	Mopeds	Child Seats
Item Profit (Price)	$500	$1500	$250

There is a fixed cost/capital allotted for acquiring each item (materials, etc…) and time (hours) allotted for the assembly as a finished sellable product. In addition, holding space/storage for the finished products awaiting sale/to be shipped has to be provided/available. This is information for each item is as follows:

	Bicycles	Mopeds	Child Seats
Capital	$300	$1200	$120
Hours	40	80	40
Storage	.5	1	.5

a.) If SDV Cycle Stop has $93,000 capital available for the month for product and has a facility/location to store 100 units (estimated based on size of the items versus available square footage) and 7680 man-hours available for product assembly (two 8 hour shifts per day, 6 days a week, for 4 weeks with 20 assemblers hired); WHAT is the MAXIMUM order size/profit that can be obtained?

b.) The following month, a more robust/compact/partially pre-assembled child seat was found from a local supplier which allows for it to offered for the same price but it only requires half the holding space/ storage (0.25) and half the assembly time (20 hours). What is the new maximum order size/profit that can be obtained with the same available capital investment and available man-power?

c.) Using the setup from part b.), how many bicycles could you make to keep the maximum profit from going below $127,000 [approximately half way between profits computed a.) and b.)] - meaning a feasible solution. HINT: Have to add 2 new constraints……

d.) Identify the differences (or not) between the three profiles including the sensitivity reports.

Solution: #1323

MAT540 Week 8 Assignment Linear Programming Case Study Complete Solution

Variables
Clearly, the unknowns in this problem are the number of units of each type of bicycle, so we define
x=number of adult bicycle units, y=Number of moped unit...