what is the optimal production plan for the year what is the annual profit from
ID: 406677 • Letter: W
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what is the optimal production plan for the year what is the annual profit from this plan what is the cost of this plan Case 1: (Q&H; Manufacturer, ver.2) Q&H; is a major detergent manufacturer with a demand forecast for the coming year as shown in the table below Month Demand Month Demand January 2,900 July 2,710 February 3,110 August 2,870 March 2,870 September 2,540 April 3,120 October 2.910 May 2.650 November 2,620 June 3,280 December 2.97 Capacity at Q&H; is governed by the number of hours the line runs. The line requires a team of 150 employees. Employees are paid $15 per hour for regular time and S25 per hour for overtime. Each ton of detergent requires one hour of operation of the line. The plant works 23 days a month, two shifts a day, and eight hours a shift of regular time. Overtime is restricted to a maximum of 25 hours per employee per month. Each ton of detergent uses $1,200 of material. Carrying a ton of detergent in inventory from one month to the next costs $120. Q&H; starts with 180 tons in inventory and wants to end with the same level. During intermediate months Q&H; wants at least 120 tons of inventory. Detergent is currently sold to retailers for $2,800 per ton (a) What is the optimal production plan for the year? What is the annual profit from this plan? What is the cost of this plan? (b) Is there any value for management to negotiate an increase of allowed overtime per employee per month from 25 hours to 40? (c) We now assume that Q&H; can change the size of the workforce by laying off or hiring employees. Hiring a new employee incurs a cost of $1,200, while laying off an employee incurs a layoff cost of S2,500. It takes an employee two months to reach full production capacity. During those two months, a new employee provides only 50 percent productivity. Anticipating a smilar demand pattern next year, Q&H; aims to end the year with 150 employees. What is the optimal production, hiring, and layoff schedule? What is the cost of such a schedule? (d) IfQ&H; could improve its training so that new employees achieve full productivity right away, how much improvement in annual cost would the company see? How is the hiring and layoff policy during the year affected by this change? (e) Now assume that a third party has offered to supply detergent to Q&H; at $2,500 per ton How does this change affect the optimal production plan? How should Q&H; use the third party if new employees provide only 50 percent productivity for the first two months? (t) How should Q&H; use the third party if new employees are able to achieve full productivity right away? Why does the use of the third party change with the productivity of new employees?Explanation / Answer
Answer: Demand for the detergent Month Demand January 2900 February 3110 March 2870 April 3120 May 2650 June 3280 July 2710 August 2870 September 2540 October 2910 November 2620 December 2970 Total demand = 34550 tons Sale price per tons = $2,880 Total revenue = $99,504,000 Cost per ton of detergent = 2640 per tons Cost of labour = 11061000 Total cost $102,273,000 Loss = $2,769,000
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