Georgia Cabinets manufactures

 

Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here:
Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3
Hours required to complete all the oak cabinets 45 41 34
Hours required to complete all the cherry cabinets 63 44 31
Hours available 35 25 30
Cost per hour $33 $41 $60
For example, Cabinetmaker 1 estimates that it will take 45 hours to complete all the oak cabinets and 63 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 35 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only complete 35/45 = 0.78, or 78%, of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 35/63 = 0.56, or 56%, of the cherry cabinets if it worked only on cherry cabinets.
a. Formulate a linear programming model that can be used to determine the proportion of the oak cabinets and the proportion of the cherry cabinets that should be given to each of the three cabinetmakers in order to minimize the total cost of completing both projects.
Let 01 = proportion of Oak cabinets assigned to cabinetmaker 1 02 = proportion of Oak cabinets assigned to cabinetmaker 2 03 = proportion of Oak cabinets assigned to cabinetmaker 3 Ci = proportion of Cherry cabinets assigned to cabinetmaker 1 C2 = proportion of Cherry cabinets assigned to cabinetmaker 2 C3 = proportion of Cherry cabinets assigned to cabinetmaker 3
Min I II 1 + 1 II 1 + 1 II II 1 + II 1 + C3 01 02 03 C Cl C2 s.t. I 01 I I Hours avail. 1 I I CI I I + 1 Hours avail. 2 I I 02 C2 1 < Hours avail. 3 1 03 C3 + 1 +1 = Oak 1 I 01 02 03 I I I I I I Cherry I I Cl C2 C3 01, 02, 03, C1, C2, C3 0
b. Solve the model formulated in part (a). What proportion of the oak cabinets and what proportion of the cherry cabinets should be assigned to each cabinetmaker? What is the total cost of completing both projects? If required, round your answers for the proportions to three decimal places, and for the total cost to two decimal places.
Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Oak 0 y = 02 = 03 = Cherry Cl = C2 = C3 =
Total Cost = $ c. If Cabinetmaker 1 has additional hours available, would the optimal solution change?
Explain.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
d. If Cabinetmaker 2 has additional hours available, would the optimal solution change?
Explain.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
e. Suppose Cabinetmaker 2 reduced its cost to $39 per hour. What effect would this change have on the optimal solution? If required, round your answers for the proportions to three decimal places, and for the total cost to two decimal places.
Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Oak 03 = 02 = 03 = Cherry Cl = C2 = C3 =
Total Cost = $ Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Sample Solution 

Transient memory is the memory for a boost that goes on for a brief time (Carlson, 2001). In reasonable terms visual transient memory is frequently utilized for a relative reason when one can’t thoroughly search in two spots immediately however wish to look at least two prospects. Tuholski and partners allude to momentary memory similar to the attendant handling and stockpiling of data (Tuholski, Engle, and Baylis, 2001). They additionally feature the way that mental capacity can frequently be antagonistically impacted by working memory limit. It means quite a bit to be sure about the typical limit of momentary memory as, without a legitimate comprehension of the flawless cerebrum’s working it is challenging to evaluate whether an individual has a shortage in capacity (Parkin, 1996).

 

This survey frames George Miller’s verifiable perspective on transient memory limit and how it tends to be impacted, prior to bringing the examination state-of-the-art and outlining a determination of approaches to estimating momentary memory limit. The verifiable perspective on momentary memory limit

 

Length of outright judgment

The range of outright judgment is characterized as the breaking point to the precision with which one can distinguish the greatness of a unidimensional boost variable (Miller, 1956), with this cutoff or length generally being around 7 + 2. Mill operator refers to Hayes memory length try as proof for his restricting range. In this members needed to review data read resoundingly to them and results obviously showed that there was a typical maximum restriction of 9 when double things were utilized. This was regardless of the consistent data speculation, which has proposed that the range ought to be long if each introduced thing contained little data (Miller, 1956). The end from Hayes and Pollack’s tests (see figure 1) was that how much data sent expansions in a straight design alongside how much data per unit input (Miller, 1956). Figure 1. Estimations of memory for data wellsprings of various sorts and bit remainders, contrasted with anticipated results for steady data. Results from Hayes (left) and Pollack (right) refered to by (Miller, 1956)

 

Pieces and lumps

Mill operator alludes to a ‘digit’ of data as need might have arisen ‘to settle on a choice between two similarly probable other options’. In this manner a basic either or choice requires the slightest bit of data; with more expected for additional complicated choices, along a twofold pathway (Miller, 1956). Decimal digits are worth 3.3 pieces each, implying that a 7-digit telephone number (what is handily recollected) would include 23 pieces of data. Anyway an evident inconsistency to this is the way that, assuming an English word is worth around 10 pieces and just 23 pieces could be recollected then just 2-3 words could be recalled at any one time, clearly mistaken. The restricting range can all the more likely be figured out concerning the absorption of pieces into lumps. Mill operator recognizes pieces and lumps of data, the qualification being that a lump is comprised of various pieces of data. It is fascinating to take note of that while there is a limited ability to recall lumps of data, how much pieces in every one of those lumps can differ generally (Miller, 1956). Anyway it’s anything but a straightforward instance of having the memorable option enormous pieces right away, fairly that as each piece turns out to be more recognizable, it tends to be acclimatized into a lump, which is then recollected itself. Recoding is the interaction by which individual pieces are ‘recoded’ and appointed to lumps.

Transient memory is the memory for a boost that goes on for a brief time (Carlson, 2001). In down to earth terms visual momentary memory is frequently utilized for a relative reason when one can’t search in two spots without a moment’s delay however wish to look at least two prospects. Tuholski and partners allude to transient memory similar to the attendant handling and stockpiling of data (Tuholski, Engle, and Baylis, 2001). They likewise feature the way that mental capacity can frequently be unfavorably impacted by working memory limit. It means a lot to be sure about the ordinary limit of momentary memory as, without a legitimate comprehension of the unblemished mind’s working it is hard to evaluate whether an individual has a shortfall in capacity (Parkin, 1996).

 

This survey frames George Miller’s verifiable perspective on transient memory limit and how it tends to be impacted, prior to bringing the exploration forward-thinking and representing a determination of approaches to estimating momentary memory limit. The authentic perspective on transient memory limit

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