A manufacturer employs three inputs: man-hours, machine-hours and cloth material to manufacture two types of dresses. Type A dress fetches the manufacturer a profit of ? (160+XX) per piece, while Type B, that of 7(180+XX) per piece. The manufacturer has enough man-hours to manufacture 50 pieces of Type A and 20 pieces of Type B dresses per day while the machine-hours the manufacturer possesses suffice only for 36 pieces of Type A or for 24 pieces for Type B dresses. Cloth material available per day is limited but sufficient enough for 30 pieces of either type of dresses. Formulae the linear programming model and solve it graphically. XX = last two digits of your roll no.
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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?A bank is trying to determine which of two machinesshould be rented to process checks. Machine 1 rents for$10,000 per year and processes 1,000 checks per hour.Machine 2 rents for $15,000 per year and processes 1,600checks per hour. Assume that the machines work 8 hours aday, 5 days a week, 50 weeks a year. The bank must processan average of 800 checks per hour, and the average checkprocessed is for $100. Assume an annual interest rate of20%. Then determine the cost to the bank (in lost interest)for each hour that a check spends waiting for and undergoingprocessing. Assuming that interarrival times and servicetimes are exponential, which machine should the bank rent?
- A brewery produces regular beer and a lower-carbohydrate Tight beer. Steady customers of the brewery buy 12 units of regular beer and 16 units of light beer monthly. While setting up the brewery to produce the beers, the management decides to produce extra beer, beyond that needed to satisfy customers. The cost per unit of regular beer is $32,000 and the cost per unit of light beer is $60,000. Every unit of regular beer brings in $100,000 in revenue, while every unit of light beer brings in $300,000 in revenue. The brewery needs at least $9,000,000 in revenue, and has determined that the total demand will be at least 50 units of beer. Complete parts (a) and (b).A company with a capacity of 3,000 units a month has fixed costs of P1,500 a month and labor costs of P10 a unit. Material costs are P5 per unit. The company has been producing at 80 percent of capacity and selling its product for P20. 1What would its net income be at 100 percent at capacity 1.2What would its net income be at 120 percent of capacity if it is assumed that 20 percent more products could be produced on overtime at an extra P3 labor cost per unit for all production above 100 percent?A furniture company manufactures chairs and desks. The sawing department cuts the lumber for both products, which is then sent to separate assembly departments. Assembled items are sent to the painting department for finishing. The daily capacity of the sawing department is 200 chairs or 80 desks. The chair assembly department can produce 120 chairs daily, and the desk assembly department 60 desks daily. The paint department has a daily capacity of either 150 chairs or 100 desks. Given that the profit per chair is $50 and that of a desk is $100. Formulate the problem as a linear program to determine the optimal product mix for the company.
- 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 14Western Chassis produces high-quality polished steel and aluminum sheeting and two lines of industrial chassis for the rack mounting of Internet routers, modems, and other telecommunications equipment. The contribution margin (contribution toward profit) for steel sheeting is $0.40 per pound and for aluminum sheeting is $0.60 per pound. Western earns $12 contribution on the sale of a Standard chassis rack and $15 contribution on a Deluxe chassis rack. During the next production cycle, Western can buy and use up to 25,800 pounds of raw unfinished steel either in sheeting or in chassis. Similarly, 20,400 pounds of aluminum are available. One standard chassis rack requires 16 pounds of steel and 8 pounds of aluminum. A Deluxe chassis rack requires 12 pounds of each metal. The output of metal sheeting is restricted only by the capacity of the polisher. For the next production cycle, the polisher can handle any mix of the two metals up to 4,000 pounds of metal sheeting. Chassis manufacture…A department works one 8-hour shift, 250 days a year, and has these figures for usage of amachine that is currently being considered:ProductAnnualDemandStandard ProcessingTime per Unit (hr)Processing TimeNeeded (hr)1 400 5.0 2,0002 300 8.0 2,4003 700 2.0 1,4005,800Units of capacity needed = Processing time needed ___________________________ Processing time capacity per unit (5–3)Working one 8-hour shift 250 days a year provides an annual capacity of 8 × 250 =2,000 hours per year. Consequently, three of these machines would be needed to handle therequired volume:5,800 hours __________________ 2,000
- Nature's Garden Inc. produces wood chips, wood pulp, and mulch. These products are produced through harvesting trees and sending the logs through a wood chipper machine. One batch of logs produces 20,304 cubic yards of wood chips, 14,100 cubic yards of mulch, and 9,024 cubic yards of wood pulp. The joint production process costs a total of $32,000 per batch. After the split-off point, wood chips are immediately sold for $25 per cubic yard while wood pulp and mulch are processed further. The market value of the wood pulp and mulch at the split-off point is estimated to be $22 and $24 per cubic yard, respectively. The additional production process of the wood pulp costs $5 per cubic yard, after which it is sold for $30 per cubic yard. The additional production process of the mulch costs $4 per cubic yard, after which it is sold for $32 per cubic yard.The ore of a gold mine in the province contains, on average, 0,5 ounce of gold per ton Method A of processing costs 150Photon and recovers 93% of the gold, while Method B costs only 120Php/ton and recovers 81% of the gold. If gold can be sold at 1,200/ounce, which method is better and by how much?each Distributors packages and distributes industrial supplies. A standard shipment can be packaged in a class A container, a class K container, or a class T container. A single class A container yields a profit of $10; a class K container, a profit of $8; and a class T container, a profit of $12. Each shipment prepared requires a certain amount of packing material and a certain amount of time. Formulate and solve this problem using LP software. Resources Needed per Standard Shipment Class of Container Packing Material (pounds) Packing Time (hours) A 2 2 K 1 6 T 3 4 Total amount of resource available per week 120 pounds 210 hours Hugh Leach, head of the firm, must decide the optimal number of each class of container to pack each week. He is bound by the previously mentioned resource restrictions but also decides that he must keep his 6 full-time packers employed all 210 hours (6 workers × 35 hours)…