The Kleenglass Corporation makes a dishwasher that has excellent cleaning power.

Question

The Kleenglass Corporation makes a dishwasher that has excellent cleaning power. This dishwasher uses less water than most competitors, and it is extremely quiet. Orders have been received from several retails stores for delivery at the end of each of the next 3 months, as shown below:
NUMBER OF
MONTH UNITS
June …………………. 195
July …………………. 215
August ………………. 205
Due to limited capacity, only 200 of these can be made each month on regular time, and the cost is $300 each. However, an extra 15 units per month can be produced if overtime is used, but the cost goes up to $325 each. Also, if there are any dishwashers produced in a month that are not sold in that month, there is a $20 cost to carry this item to the next month. Use linear programming to determine how many units to produce in each month on regular time and on overtime to minimize the total cost while meeting the demands.

This must be completed in excel...

Explanation / Answer

I am not able to post the Excel solution here. I will explain the approach for the question.

We know, 200 units can be produced on a regular basis in a month with a unit cost of $300. For extra units (maximum 15) produced in a month, the unit cost goes up to $325. Thus, there is $25 increase in the cost. Now, if you produce the extra units for the next month in regular time, you will have a cost increase of $20 per unit and if the same is done in overtime, there will be a cost increase of $25 + $20 = $45.

Now, in June there is a demand of 195 units. As we can produce 200 units in regular time and the cost of producing a unit in regular time for the next month ($20) is less than the cost incurred on producing the same in the next month in overtime ($25), we will produce 200 units and carry forward the extra 5 units to the next month.

So, the total cost for June = 200*300 + 5*20 = $60100.

Now, in July there is a demand for 215 units, and we have 5 units from the previous month. So, we will produce 200 units in regular time and 10 units in over time.

Note: We did not produce the extra units (5 more for the next month) in overtime because of that, the unit cost goes up by $45 which is more than producing extra units in the same month $25.

Total cost for July = 200*300 + 10*325 = $63250.

For August, we need 205 units. We have no carry forward of units here and hence, we will produce 200 units in regular time and 5 units in overtime.

Total cost for August = 200*300 + 5*325 = $61625.

Total Cost = Sum of the costs for the three months = $184975.

Month wise units in the format: Month (RegularTime Units, OverTime Units)

June (200, 0)

July (200, 10)

August (200, 5)

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