Omaha’s factory has yet another type of cost structure. Its cost function is provided graphically. Its maximum capacity is 38,00
0 units per day.
At what rate is the cost per unit decreasing for production levels above 12,000?(5 points)
State the function for the domain over [12000, 38000]. (10 points)
What is the cost per unit at the production level of 19,000? (5 points)
Omaha’s city council approved a special growth incentive that decreases the company’s tax burden for production levels above last year’s average. Explain how this is reflected by the Cost Function for Omaha’s factory.
Analysis and Making Production Decisions
You have now provided your company’s management with powerful tools that model the cost of production in the three factories. When you get an order for a certain number of units, you can be informed of the cost that would be incurred by each factory if chosen to fulfill the order. In reality, the decision must also consider many other factors, but in our scenario, we want to fill our orders at the lowest average cost per unit. Consider each of the following questions as a separate, unrelated day of business.
On Monday, you have a single request: Order A for 15,000 units. It must be fulfilled by a single factory. To which factory do you send the order? Explain your decision. Support your argument with numbers. (10 points)
On Tuesday, you have two orders. You may send each order to a separate factory OR both to the same factory. If they are both sent to be fulfilled by a single factory, you must use the total of the two orders to find that factory’s cost per unit for production on this day. Remember that the goal is to end the day with the lowest cost per unit to produce the company’s products. Order B is 7,000 units, and Order C is 30,000 units. (15 points, 5 points per part)
First, consider giving the orders to separate factories. Use these values and the following formula to calculate the average weighted cost per unit.
((cost per unit B)(#of units)+(cost per unit C)(#of units))/(Total # of units)
Second, consider sending both orders to a single factory that has the lowest cost per unit to produce 37,000 units.
Compare the two options. Decide how you will send the orders out, and document your decision by completing the daily production report below.
Production Report for Tuesday
Order # of Units Factory
B 7,000 ______
C 30,000 ______
Total # of units produced for the company today: ______
Average cost per unit for all production today: ______
At what rate is the cost per unit decreasing for production levels above 12,000?(5 points)
State the function for the domain over [12000, 38000]. (10 points)
What is the cost per unit at the production level of 19,000? (5 points)
Omaha’s city council approved a special growth incentive that decreases the company’s tax burden for production levels above last year’s average. Explain how this is reflected by the Cost Function for Omaha’s factory.
Analysis and Making Production Decisions
You have now provided your company’s management with powerful tools that model the cost of production in the three factories. When you get an order for a certain number of units, you can be informed of the cost that would be incurred by each factory if chosen to fulfill the order. In reality, the decision must also consider many other factors, but in our scenario, we want to fill our orders at the lowest average cost per unit. Consider each of the following questions as a separate, unrelated day of business.
On Monday, you have a single request: Order A for 15,000 units. It must be fulfilled by a single factory. To which factory do you send the order? Explain your decision. Support your argument with numbers. (10 points)
On Tuesday, you have two orders. You may send each order to a separate factory OR both to the same factory. If they are both sent to be fulfilled by a single factory, you must use the total of the two orders to find that factory’s cost per unit for production on this day. Remember that the goal is to end the day with the lowest cost per unit to produce the company’s products. Order B is 7,000 units, and Order C is 30,000 units. (15 points, 5 points per part)
First, consider giving the orders to separate factories. Use these values and the following formula to calculate the average weighted cost per unit.
((cost per unit B)(#of units)+(cost per unit C)(#of units))/(Total # of units)
Second, consider sending both orders to a single factory that has the lowest cost per unit to produce 37,000 units.
Compare the two options. Decide how you will send the orders out, and document your decision by completing the daily production report below.
Production Report for Tuesday
Order # of Units Factory
B 7,000 ______
C 30,000 ______
Total # of units produced for the company today: ______
Average cost per unit for all production today: ______
2 answers:
1. To find the rate of the cost per unit's decrease we need to find the slope of the graph for production levels above 12,000. We find the slope by dividing the change in y over the change in x. The two points that we will utilize for calculating the slope are the given points (12000, 0.85) and (38000, 0.59).
ANSWER: The rate of decrease is 0.00001 dollars per unit.
2. The function for the domain [12000, 38000] is just a linear equation that follows the form y = mx + b where m is the slope and b is the y-intercept. Since we have already calculated for the slope in the previous item, we will just compute the y-intercept. We will do this by using the point (38000,0.59) as our test point.
ANSWER: The function will then be
3. To know what the cost per unit when the company has produced 19,000 units already, we just use the function that we have built in the previous item. For this scenario, the value of x would be 19,000 and we are tasked to solve for y.
ANSWER: The cost per unit at the production level of 19,000 is 0.78 dollars.
4. This special growth incentive can be seen on the graph thru the decreasing cost per unit after the production level of 12,000. We can only assume that last year's average were 12,000 units therefore exceeding that production level decreases the cost per unit since the company's tax burden is decreased.
5. For questions 5 and 6 I have found the graph/function for the Seattle and Wichita Factory. They are attached here, respectively.
Knowing the cost per unit for every factory, we just compare the cost and pick the lowest one.
Wichita: $1
Seattle: $0.75
Omaha:
ANSWER: We will send the order to the Seattle factory since they have the lowest cost per unit.
6a. For this subitem we are tasked to compare the cost per unit if we were to send two orders to a combination of any two factories. We will just find the cost per unit for every combination and show the average weighted cost by following the given formula.
Combination 1
Wichita: 7,000 units = $1
Seattle: 30,000 units = $0.68
Average Cost: $0.74
Combination 2
Wichita: 7,000 units = $1
Omaha: 30,000 units = $0.67
Average Cost: $0.73
Combination 3
Seattle: 7,000 units = $0.35
Omaha: 30,000 units = $0.67
Average Cost: $0.61
Combination 4
Omaha: 7,000 units = $0.85
Seattle: 30,000 units = $0.68
Average Cost: $0.71
Combination 5
Omaha: 7,000 units = $0.85
Wichita: 30,000 units = $0.80
Average Cost: $0.81
Combination 6
Seattle: 7,000 units = $0.35
Wichita: 30,000 units = $0.80
Average Cost: $0.71
6b. For this subitem we need to give all 37,000 units to one factory. We just need to calculate the cost per unit for every function. The calculation for the three factories is shown below (except when no calculation is needed, only inspection of the graph or function):
Wichita: not defined
Seattle:
Omaha:
6c. For this item, we will review our answers for the two previous subitems and select the one with the lowest cost per unit. Upon examining, we can see that letting Omaha produce all 37,000 units will yield the lowest cost.
ANSWER: Orders B and C should be produced by Omaha's factory.
Total # of units produced for the company today: 37,000
Average cost per unit for all production today: $0.60
ANSWER: The rate of decrease is 0.00001 dollars per unit.
2. The function for the domain [12000, 38000] is just a linear equation that follows the form y = mx + b where m is the slope and b is the y-intercept. Since we have already calculated for the slope in the previous item, we will just compute the y-intercept. We will do this by using the point (38000,0.59) as our test point.
ANSWER: The function will then be
3. To know what the cost per unit when the company has produced 19,000 units already, we just use the function that we have built in the previous item. For this scenario, the value of x would be 19,000 and we are tasked to solve for y.
ANSWER: The cost per unit at the production level of 19,000 is 0.78 dollars.
4. This special growth incentive can be seen on the graph thru the decreasing cost per unit after the production level of 12,000. We can only assume that last year's average were 12,000 units therefore exceeding that production level decreases the cost per unit since the company's tax burden is decreased.
5. For questions 5 and 6 I have found the graph/function for the Seattle and Wichita Factory. They are attached here, respectively.
Knowing the cost per unit for every factory, we just compare the cost and pick the lowest one.
Wichita: $1
Seattle: $0.75
Omaha:
ANSWER: We will send the order to the Seattle factory since they have the lowest cost per unit.
6a. For this subitem we are tasked to compare the cost per unit if we were to send two orders to a combination of any two factories. We will just find the cost per unit for every combination and show the average weighted cost by following the given formula.
Combination 1
Wichita: 7,000 units = $1
Seattle: 30,000 units = $0.68
Average Cost: $0.74
Combination 2
Wichita: 7,000 units = $1
Omaha: 30,000 units = $0.67
Average Cost: $0.73
Combination 3
Seattle: 7,000 units = $0.35
Omaha: 30,000 units = $0.67
Average Cost: $0.61
Combination 4
Omaha: 7,000 units = $0.85
Seattle: 30,000 units = $0.68
Average Cost: $0.71
Combination 5
Omaha: 7,000 units = $0.85
Wichita: 30,000 units = $0.80
Average Cost: $0.81
Combination 6
Seattle: 7,000 units = $0.35
Wichita: 30,000 units = $0.80
Average Cost: $0.71
6b. For this subitem we need to give all 37,000 units to one factory. We just need to calculate the cost per unit for every function. The calculation for the three factories is shown below (except when no calculation is needed, only inspection of the graph or function):
Wichita: not defined
Seattle:
Omaha:
6c. For this item, we will review our answers for the two previous subitems and select the one with the lowest cost per unit. Upon examining, we can see that letting Omaha produce all 37,000 units will yield the lowest cost.
ANSWER: Orders B and C should be produced by Omaha's factory.
Total # of units produced for the company today: 37,000
Average cost per unit for all production today: $0.60
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