Jenny Company produces two types of pants: long pants and short pants. The cost of making a pair of short pants and a pair of long pants are RM 75 and RM 95 respectively. In one week, the company must produce at least 150 pants of cach type. The minimum weekly production is 500 pants. The short pants is sold for RM 120 cach and the long pants for RM 150 cach. Using the graphical method, find: a) The number of short pants and long pants to be made in a week in order to minimize the total production cost. b) The profit made at the minimum weekly production cost.
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?The manager of the deli section of a grocery superstore has just learned that the department has112 pounds of mayonnaise, of which 70 pounds is approaching its expiration date and must beused. To use up the mayonnaise, the manager has decided to prepare two items: a ham spread anda deli spread. Each pan of the ham spread will require 1.4 pounds of mayonnaise, and each panof the deli spread will require 1.0 pound. The manager has received an order for 10 pans of hamspread and 8 pans of the deli spread. In addition, the manager has decided to have at least 10 pansof each spread available for sale. Both spreads will cost $3 per pan to make, but ham spread sellsfor $5 per pan and deli spread sells for $7 per pan.a. Determine the solution that will minimize cost.b. Determine the solution that will maximize profit.
- Production and Materials Purchases Budgets White Corporation’s budget calls for the following sales for next year:Quarter 1 90,000 units Quarter 3 68,000 unitsQuarter 2 76,000 units Quarter 4 96,000 unitsEach unit of the product requires 3 pounds of direct materials. The company’s policy is to begineach quarter with an inventory of product equal to 5% of that quarter’s estimated sales requirementsand an inventory of direct materials equal to 20% of that quarter’s estimated direct materials requirements for production.Required Determine the production and materials purchases budgets for the second quarter.Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pens are given below. The profit for either model is $1000 per lot. Fliptop Model Tiptop Model Available Plastic 3 4 36 Ink Assembly 5 4 40 Molding Time 5 2 30 Formulate a LP Model for this problem.Cantel Company produces cleaning compounds for both commercial and household customers. Some of these products are produced as part of a joint manufacturing process. For example, GR37, a coarse cleaning powder meant for commercial sale, costs $1.90 a pound to make and sells for $2.00 per pound. A portion of the annual production of GR37 is retained for further processing in a separate department where it is combined with several other ingredients to form SilPol, which is sold as a silver polish, at $5.00 per unit. The additional processing requires 1/4 pound of GR37 per unit; additional processing costs amount to $3.90 per unit of SilPol produced. Variable selling costs for SilPol average $0.50 per unit. If production of SilPol were discontinued, $1,000 of costs in the processing department would be avoided. Cantel has, at this point, unlimited demand for, but limited capacity to produce, product GR37. Required: 1. Calculate the minimum number of units of SilPol that would have to be…
- 2. A firm makes two products X and Y and has a total production capacity of 9 tons per day.X and Y requiring the same production capacity. The same has a permanent contract to supply at least two tons of X and at least 3 tons of Y per day to another company. Each ton of X requires 20 machine hours of production time and each ton of Y requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. The entire firm's output can be sold and profit made is 80 R.O of X and 120 R.O per ton of Y. It is required to determine the production schedule for maximum profit and to calculate this profit. Formulate a LPP.A firm has revenue function given by R=10Q where R=Gross Revenue and Q=Numberof Units Sold, Production Cost function is given byC = 20000+ 50(Q/800)^2Find:(i) the total Profit function, and(ii) the number of Units (Q) to be sold to get the maximum ProfitYou own wheat warehouse with capacity of 20,000 bushels. At the beginning of month 1, you have 6,000 bushels of wheat. Each month, wheat can be bought and sold at the price per 1000 bushels given in the table Month Selling price ($) Purchase prie ($) 1 3 8 2 6 8 3 7 2 4 1 3 5 4 4 6 5 3 7 5 3 8 1 2 9 3 5 10 2 5 The sequence of events during each month is as follows: a. You observe your initial stock of wheat. b. You can sell any amount of wheat up to your initial stock at the current month's selling price. c. You can buy(at the current month's buying price) as much wheat as you want, subject to the warehouse size imitation. Your goal is to formulate an LP that can be used to determine how to maximise the profit earned over the next 10 months and solve using Excel solver or AMPL
- Grey Manufacturing Company expects sales to total 13,000 units in the first quarter, 12,000 units inthe second quarter, and 15,000 units in the third quarter of the current fiscal year. Company policyis to have on hand at the end of each quarter an amount of inventory equal to 10% of the followingquarter’s sales. Given this information, how many units should be scheduled for production in thesecond quarter?ABC Cabinets received a contract to produce bookshelf speakers (BS) and floor speakers (FS) over the next 2months. The contract says ABC must deliver 2100 BS and 1500 FS at the end of month 1 and deliver 1200 BS and2600 FS at end of month 2. The time to make a BS is 0.7hr and a FS is 1hr. Raw material costs $10 for each BSand $12 for each FS and there is an unlimited amount available. Labor costs are $22/hr using regular productiontime and $33/hr using overtime. ABS has up to 2400hrs of regular production time each month and up to 1000additional hours of overtime each month. Any cabinets left at the end of month 1 can be stored for $5/cabinet.(a) Formulate an LP to determine the number of units that should be manufactured each month on regular andovertime to minimize total production and storage costsMaxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pen...Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pens are given below.Fliptop Model Tiptop Model AvailablePlastic 3 4 36Ink Assembly 5 4 40Molding Time 5 2 30The profit for either model is $1000 per lot.What is the linear programming model for this problem?What are the boundary points of the feasible region?What is the profitability at each boundary point of the feasible region?Find the optimal solution.