Kahuna Industries has two manufacturing departments--Fabrication and Finishing. The company used the following data at the begin
1 answer:
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Answer:
The Linear programming model is given as below
Profit Function:
Constraints:
Explanation:
As the question is not complete, the complete question is found online and is attached herewith.
Let the number of product 1 to be produced is X, that of product 2 is Y and product 3 is Z
so the maximizing function is the profit function which is given as
Now as the number of hours in a week are 40 and there are a total of 10 type 1 machines so the total number of machine 1 hours are 40*10=400 hours
As from the given table product 1 uses 2 machine hours of machine 1, product 2 uses 2 machine hours of machine 1 and product 3 uses 1 hour of machine 1 so
Now as the number of hours in a week are 40 and there are a total of 6 type 2 machines so the total number of machine 2 hours are 40*6=240 hours
As from the given table product 1 uses 3 machine hours of machine 2, product 2 uses 4 machine hours of machine 2 and product 3 uses 6 hour of machine 2 so
Now as the number of hours in a week are 40 and there are a total of 8 type 3 machines so the total number of machine 3 hours are 40*8=320 hours
As from the given table product 1 uses 4 machine hours of machine 3, product 2 uses 6 machine hours of machine 3 and product 3 uses 5 hour of machine 3 so
Now as the machine 1 is used as 2X+2Y+Z in a week and the week is of 40 hours so the number of machines to be used are given as
Now as the machine 2 is used as 3X+4Y+6Z in a week and the week is of 40 hours so the number of machines to be used are given as
Now as the machine 3 is used as 4X+6Y+5Z in a week and the week is of 40 hours so the number of machines to be used are given as
Now the workers are available for 35 hours so the worker available at the machine 1 is given as
That of machine 2 is given as
That of machine 3 is given as
As the total number of workers is 19 so the constraint is given as
So the Linear programming model is given as below
Profit Function:
Constraints:
Answer: d. $1,534 positive net present value of the cash flows. Based on present value considerations, Dobson Construction should buy the machine.
Explanation:
To calculate the Net Present Value, we take the present values of all the future cashflows and subtract the initial cost from this amount.
Now, the cashflows are stable and this means that we can use the Present Value of an Annuity factor to find out the present value of the cashflows. We can then use a simple present value formula to find out the PV of the sale price.
I have attached a table that shows the PVIFA factors to make our calculations easier.
With interest rates at 12% and the year being 8 years, the PVIFA factors is 4.9676
Calculating therefore we have,
= 15,000 * 4.9676
= $74,514
This is the present value of 8 years of $15,000 cash flows.
In the same year, the machine can be sold for $5,000 so the present value of that is,
= 5000 / ( 1 + 12%)^8
= $2,020
Adding those together we get,
= 74,514 + 2,020
= 76,534
= $76,534
Subtracting the original cost we have,
= 76,534 - 75,000
= $1,534 in positive cashflow.
Net Present Value = $1,534
This means that Based on present value considerations, Dobson Construction should buy the machine due to a $1,534 positive net present value.
