Your answer will be the number of ProLine nailers to be produced
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- 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?In the lawn mower production problem in Example 8.4, experiment with the penalty cost for unsatisfied pickups in week 1. If this cost is sufficiently small, does the company ever produce fewer than seven models in week 1 and allow some week 1 pickups to be unsatisfied?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.
- The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Can you guess the results of a sensitivity analysis on the initial inventory in the Pigskin model? See if your guess is correct by using SolverTable and allowing the initial inventory to vary from 0 to 10,000 in increments of 1000. Keep track of the values in the decision variable cells and the objective cell.The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. As indicated by the algebraic formulation of the Pigskin model, there is no real need to calculate inventory on hand after production and constrain it to be greater than or equal to demand. An alternative is to calculate ending inventory directly and constrain it to be nonnegative. Modify the current spreadsheet model to do this. (Delete rows 16 and 17, and calculate ending inventory appropriately. Then add an explicit non-negativity constraint on ending inventory.)The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Modify the Pigskin model so that there are eight months in the planning horizon. You can make up reasonable values for any extra required data. Dont forget to modify range names. Then modify the model again so that there are only four months in the planning horizon. Do either of these modifications change the optima] production quantity in month 1?
- In Example 11.3, suppose you want to run five simulations, where the probability of passing inspection is varied from 0.6 to 1.0 in increments of 0.1. Use the RISKSIMTABLE function appropriately to do this. Comment on the effect of this parameter on the key outputs. In particular, does the probability of passing inspection have a large effect on when production should start? (Note: When this probability is low, it might be necessary to produce more than 25 batches, the maximum built into the model. Check whether this maximum should be increased.)(Need both parts a and b) During the next four months, a customer requires, respectively, 500, 650, 1000, and 700 units of a commodity, and no backlogging is allowed (that is, the customer’s requirements must be met on time). Production costs are $50, $80, $40, and $70 per unit during these months. The storage cost from one month to the next is $20 per unit (assessed on ending inventory). It is estimated that each unit on hand at the end of month 4 can be sold for $60. Assume there is no beginning inventory. A. What is the objective function in this problem? B. What are the constraints in this problem? Write algebraic expressions for eachAnswer Questions a to e, based on the following information You run a small grocery store and have the following fruits in storage: 1000 apples, 1500 oranges, 75 watermelons, 100 peaches, and 125 mangos. You plan to package these fruits into gift sets and sell them during the New Year's Sale. The gift sets will be offered in 3 options. Each option is sold at a different price and subject to the following requirements in terms of the fruits that are in the bag: . Option A-Must contain 6 apples, 6 oranges, and 1 watermelon. Option B-Must contain 2 apples, 4 oranges, 1 peach, and 2 mangos. Option C-Must contain 1 watermelon, 1 peach, and 1 mango. Option A will sell for $100, option B will sell for $130, and option C will sell for $200. Assume that there is no limit on demand and that we allow fractional gift sets for simplicity. Your goal is to maximize revenue. Suppose we would like to formulate this as a LP problem, and have the following decision variables: TA =# of gift set A, B =# of…
- ProHaul specializes in trans-American shipments for businesses through the delivery of containers. For every container the company loads on its trucks, ProHaul estimates the haul costs $1,000. In addition, containers are weighed and for each pound, there are hauling fees of $0.15. ProHaul plans to charge $0.49 per pound to his customers.The company finds out that to maintain the integrity of its containers, each container could only hold an average of 8,000 pounds. What would the company have to charge customers to make $5,000 in profit on each container?Happy Dog Inc. produces three types of dog food. Puppy Blend is produced for dogs that are less than a year old, Adult Blend for dogs between 1 and 8 years old, and Geriatric Blend for dogs older than 8 years. Each blend, sold in 5 pound bags, has a unique recipe that requires, among other ingredients, exact quantities of certain raw materials. Chicken Fish Meal Soy Flour Demand (in5 lb. bags) Puppy Blend Adult Blend Geriatric Blend Availability of rawmaterial 2.5 lbs. 1.5 lbs. 1.0 lbs. 10,000 lbs. 1.0 lbs. 2.0 lbs. 2.0 lbs. 20,000 lbs. 0.5 lbs. 0.5 lbs. 1.0 lbs. 5,000 lbs. 2000 8000 1000 a. Formulate a linear programming model that produces as many bags of dog food as possible without exceeding the demand or the available supply of raw material.b. Reformulate the linear programming model if the company is now interested in maximizing their profit 1price - raw material cost2 from dog food production. Assume that Puppy Blend sells for $9.50 per bag, Adult Blend…Patz Company produces two types of machine parts: Part A and Part B, with unit contribution margins of $400 and $800, respectively. Assume initially that Patz can sell all that is produced of either component. Part A requires two hours of assembly, and B requires five hours of assembly. The firm has 400 assembly hours per week. What if market conditions are such that Patz can sell at most 100 units of Part A and 80 units of Part B? Express the objective function with its associated constraints for this case. Objective function: Max Z = $400 A + $800 B Assembly-hour constraint fill in the blank 7 A + fill in the blank 8 B ≤ fill in the blank 9 Demand constraint for Part A A ≤ fill in the blank 10 Demand constraint for Part B B ≤ fill in the blank 11 Identify the optimal mix and its associated total contribution margin.Component A $fill in the blank 12 units Component B $fill in the blank 13 units Total contribution $fill in the blank 14