5. A mixture of pellets is to be made containing x regular pellets, y large pellets and z extra large pellets. Cost, weight and volume data for each type of pellet are shown in the table. Is it possible to make mixture of 55 pellets at a cost of $0.85 if the mixture is to have 120 weight units and 130 volume units? If so, how many each type of pellet should be in the mixture? Pellet Type Cost per Pellet in Cents Weight Units per Pellet Number of Volume Pellets Units per Pellet Regular Large Extra large 1 4 y 3 2 2 1 4 3
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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.If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.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 Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.A small candy shop is preparing for the holiday season. The owner must decide how many bags of deluxe mix and how many bags of standard mix of Peanut/Raisin Delite to put up. The deluxe mix has .70 pounds of raisins and .30 pounds of peanuts, and the standard mix has 0.45 pounds of raisins and 0.55 pounds of peanuts per bag. The shop has 90 pounds of raisins and 60 pounds of peanuts to work with. Peanuts cost $0.6 per pound and raisins cost $1.55 per pound. The deluxe mix will sell for $2.9 for a one-pound bag, and the standard mix will sell for $2.55 for a one-pound bag. The owner estimates that no more than 110 bags of one type can be sold. a. If the goal is to maximize profits, how many bags of each type should be prepared? b. What is the expected profit?
- 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 14The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both rquire a certain amount of wiring and drilling. Each air condtioner takes 3 hours of wiring and 2 hours of drilling. During the next production period, 240 hours of wiring time are available, and up to 140 hours of drilling time may be used. Each air conditioner sold yieds a profit of $25. Each fan assembled may be sold for a $15 profit. Formulate the best combination of air conditioners and fans that yiedls the highest profit. Use the corner point graphical approach.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.
- FarmFresh Foods manufactures a snack mix called TrailTime by blending three ingredients: a dried fruit mixture, a nut mixture, and a cereal mixture. Information about the three ingredients (per ounce) is shown below. Ingredient Cost Volume Fat Grams Calories Dried fruit 0.35 0.25 cup 0 150 Nut mix 0.50 0.375 cup 10 400 Cereal mix 0.20 1 cup 1 50 Let D = number of ounces of dried fruit mix in the blend; N = number of ounces of nut mix in the blend ; C = number of ounces of cereal mix in the blend. The constraint that would ensure the mixture has no more than 25 grams of fat is:Dana’s Ribbon World makes award rosettes. Following is information about the company: Variable cost per rosette $ 2.00 Sales price per rosette $ 6.00 Total fixed costs per month $ 6000.00 Required: 1. Suppose Dana’s would like to generate a profit of $1,120. Determine how many rosettes it must sell to achieve this target profit. 2. If Dana’s sells 2,140 rosettes, compute its margin of safety in units, in sales dollars, and as a percentage of sales. 3. Calculate Dana’s degree of operating leverage if it sells 2,140 rosettes. 4a. Using the degree of operating leverage, calculate the change in Dana’s profit if unit sales drop to 1,819 units. 4b. Prepare a new contribution margin income statement to verify change in dana's profit.Dr. Thompson makes three bean mixes for coffee shops located in the Austin. The three mixes, referred to as the Tameka Mix, the Christian Mix, and the Tamia Mix, are made by mixing different percentages of five types of beans. In preparation for the fall season, Dr. Thompson just purchased the following shipments of beans at the prices shown: Type of Beans Shipment Amount in pounds Cost Per Shipment in dollars Arabica 6000 7500 Robusta 7500 7125 Liberica 7500 6750 Excelsa 6000 7200 Juno 7500 7875 The Tameka Mix consists of 15% Arabica, 25% Robusta beans, 25% Liberica, 10% Excelsa, and 25% Juno. The Christian Mix consists of 20% of each type of beans, and the Tamia Mix consists of 25% Arabica, 15% Robusta beans, 15% Liberica, 25% Excelsa, and 20% Juno. Dr. Thompson analyzed the cost to get the beans ready and determined that the profit contribution per pound is $1.65 for the Tameka Mix, $2.00 for the Christian Mix, and $2.25 for the…