Edwards Manufacturing Company purchases two component parts from three different suppliers

Problem 9-11 (Algorithmic)

Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows:

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Supplier
Component123
$10$10$15
$11$10$10

Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows:

Supplier
Capacity5751025875

If the Edwards production plan for the next period includes 1050 units of component 1 and 775 units of component 2, what purchases do you recommend? That is, how many units of each component should be ordered from each supplier?

Supplier
123
Component 1fill in the blank 1fill in the blank 2fill in the blank 3
Component 2fill in the blank 4fill in the blank 5fill in the blank 6

What is the total purchase cost for the components?

$  fill in the blank 7

Component 2fill in the blank 4fill in the blank 5fill in the blank 6

What is the total purchase cost for the components?

$  fill in the blank 7

Problem 15-9 (Algorithmic)

Marty’s Barber Shop has one barber. Customers have an arrival rate of 2.3 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions:

  1. What is the probability that no units are in the system? If required, round your answer to four decimal places.
    P0 = fill in the blank 1
  2. What is the probability that one customer is receiving a haircut and no one is waiting? If required, round your answer to four decimal places.
    P1 = fill in the blank 2
  3. What is the probability that one customer is receiving a haircut and one customer is waiting? If required, round your answer to four decimal places.
    P2 = fill in the blank 3
  4. What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.
    P3 = fill in the blank 4
  5. What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.
    P(More than 2 waiting) = fill in the blank 5
  6. What is the average time a customer waits for service? If required, round your answer to four decimal places.
    Wq = fill in the blank 6 hours

Problem 15-7 (Algorithmic)

Speedy Oil provides a single-server automobile oil change and lubrication service. Customers provide an arrival rate of 4.5 cars per hour. The service rate is 6 cars per hour. Assume that arrivals follow a Poisson probability distribution and that service times follow an exponential probability distribution.

  1. What is the average number of cars in the system? If required, round your answer to two decimal places
    L = fill in the blank 1
  2. What is the average time that a car waits for the oil and lubrication service to begin? If required, round your answer to two decimal places.
    Wq = fill in the blank 2 hours
  3. What is the average time a car spends in the system? If required, round your answer to two decimal places.
    W = fill in the blank 3 hours
  4. What is the probability that an arrival has to wait for service? If required, round your answer to two decimal places.
    Pw = fill in the blank 4

Problem 12-27 (Algorithmic)

Andalus Furniture Company has two manufacturing plants, one at Aynor and another at Spartanburg. The cost in dollars of producing a kitchen chair at each of the two plants is given here.

Aynor: Cost = 80Q1 + 5Q12 + 106
Spartanburg: Cost = 28Q2 + 3Q22 + 158

Where
Q1 = number of chairs produced at Aynor
Q2= number of chairs produced at Spartanburg

Andalus needs to manufacture a total of 30 kitchen chairs to meet an order just received. How many chairs should be made at Aynor and how many should be made at Spartanburg in order to minimize total production cost? When required, round your answers to the nearest dollar.

The optimal solution is to produce fill in the blank 1 chairs at Aynor for a cost of $  fill in the blank 2 and fill in the blank 3 chairs at Spartanburg for a cost of $  fill in the blank 4. The total cost is $  fill in the blank 5.

Problem 11-9 (Algorithmic)

Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2300, and the cost required to set up the production line for the 6-cylinder connecting rods is $3400. Manufacturing costs are $14 for each 4-cylinder connecting rod and $18 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If there is a production changeover from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 5600 6-cylinder connecting rods and 7800 4-cylinder connecting rods.

Let
x4 = the number of 4-cylinder connecting rods produced next week
x6 = the number of 6-cylinder connecting rods produced next week
s4= 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise
s6 = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise

  1. Using the decision variables x4 and s4, write a constraint that limits next week’s production of the 4-cylinder connecting rods to either 0 or 7800 units.
    fill in the blank 1x4  fill in the blank 3s4
  2. Using the decision variables x6 and s6, write a constraint that limits next week’s production of the 6-cylinder connecting rods to either 0 or 5600 units.
    fill in the blank 4x6  fill in the blank 6s6
  3. Write three constraints that, taken together, limit the production of connecting rods for next week.
    fill in the blank 7x4  fill in the blank 9s4
    fill in the blank 10x6  fill in the blank 12s6
    fill in the blank 13s4 + fill in the blank 14s6  fill in the blank 16
  4. Write an objective function for minimizing the cost of production for next week.
    Min fill in the blank 17x4 + fill in the blank 18x6 + fill in the blank 19s4 + fill in the blank 20s6

Problem 9-15

Bay Oil produces two types of fuels (regular and super) by mixing three ingredients. The major distinguishing feature of the two products is the octane level required. Regular fuel must have a minimum octane level of 90 while super must have a level of at least 100. The cost per barrel, octane levels, and available amounts (in barrels) for the upcoming two-week period are shown in the following table. Likewise, the maximum demand for each end product and the revenue generated per barrel are shown.

Develop and solve a linear programming model to maximize contribution to profit.

LetRi = the number of barrels of input i to use to produce Regular, i=1,2,3
Si = the number of barrels of input i to use to produce Super, i=1,2,3

If required, round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

Maxfill in the blank 1R1fill in the blank 2R2fill in the blank 3R3fill in the blank 4S1fill in the blank 5S2fill in the blank 6S3
s.t.
fill in the blank 7R1fill in the blank 8S1fill in the blank 9
fill in the blank 10R2fill in the blank 11S2fill in the blank 12
fill in the blank 13R3fill in the blank 14S3fill in the blank 15
fill in the blank 16R1fill in the blank 17R2fill in the blank 18R3fill in the blank 19
fill in the blank 20S1fill in the blank 21S2fill in the blank 22S3fill in the blank 23
fill in the blank 24R1fill in the blank 25R2fill in the blank 26R3fill in the blank 27R1fill in the blank 28R2fill in the blank 29R3
fill in the blank 30S1fill in the blank 31S2fill in the blank 32S3fill in the blank 33S1fill in the blank 34S2fill in the blank 35S3

R1, R2, R3, S1, S2, S3 ≥ 0

What is the optimal contribution to profit?

Maximum Profit = $  fill in the blank 36 by making fill in the blank 37 barrels of Regular and fill in the blank 38 barrels of Super.

Problem 10-09 (Algorithmic)

The Ace Manufacturing Company has orders for three similar products:

ProductOrder (Units)
1750
500
1100

Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are as follows:

MachineCapacity (Units)
1550
1450
1150
Product
MachineABC
$0.80$1.30$0.70
$1.40$1.30$1.50
$0.80$0.80$1.20

Use the transportation model to develop the minimum cost production schedule for the products and machines. Show the linear programming formulation. If required, round your answers to one decimal place.

The linear programming formulation and optimal solution are shown.

Letx1AUnits of product A on machine 1
x1BUnits of product B on machine 1
x3CUnits of product C on machine 3
Minfill in the blank 1x1Afill in the blank 2x1Bfill in the blank 3x1Cfill in the blank 4x2Afill in the blank 5x2Bfill in the blank 6x2Cfill in the blank 7x3Afill in the blank 8x3Bfill in the blank 9x3C
s.t.
fill in the blank 10x1Afill in the blank 11x1Bfill in the blank 12x1Cfill in the blank 13
fill in the blank 14x2Afill in the blank 15x2Bfill in the blank 16x2Cfill in the blank 17
fill in the blank 18x3Afill in the blank 19x3Bfill in the blank 20x3Cfill in the blank 21
fill in the blank 22x1Afill in the blank 23x2Afill in the blank 24x3Afill in the blank 25
fill in the blank 26x1Bfill in the blank 27x2Bfill in the blank 28x3Bfill in the blank 29
fill in the blank 30x1Cfill in the blank 31x2Cfill in the blank 32x3Cfill in the blank 33
xij ≥ 0 for all ij
Optimal SolutionUnitsCost
1-Afill in the blank 34$fill in the blank 35
1-Bfill in the blank 36$fill in the blank 37
1-Cfill in the blank 38fill in the blank 39
2-Afill in the blank 40fill in the blank 41
2-Bfill in the blank 42$fill in the blank 43
2-Cfill in the blank 44$fill in the blank 45
3-Afill in the blank 46fill in the blank 47
3-Bfill in the blank 48fill in the blank 49
3-Cfill in the blank 50$fill in the blank 51
Total $fill in the blank 52

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