A manufacturer makes two products P1 and P2 using two machines M1 and M2. Product P1 requires 5 hours on M1 and no time on M2, Product P2 requires 1 hour on M1 and 3 hours on M2. There are 16 hours of timer per day available on M1 and 30 hours on M2. The profit margin from P1 and P2 is Rs. 2 and Rs.10 per unit respectively. What should be the daily production mix to maximize profit?
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- Solve the following linear programming problem using simplex method.
A manufacturer makes two products P1 and P2 using two machines M1 and M2. Product P1 requires 5 hours on M1 and no time on M2, Product P2 requires 1 hour on M1 and 3 hours on M2. There are 16 hours of timer per day available on M1 and 30 hours on M2. The profit margin from P1 and P2 is Rs. 2 and Rs.10 per unit respectively. What should be the daily production mix to maximize profit?
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- 4) The making of rivet holes in structural steel members can be done by 2 methods. The first method consists of laying out the position of the holes in the members and using a drill press costing P100k. The machinist is paid P60 per hour and he can drill 80 holes per hour. The second method makes use of a multiple-punch machine costing P80k. The punch operator is paid P40 an hour and he can punch out 1 hole for 3 seconds. This method also requires an expense of P1.25 per hole to set the machine. (a) if all other costs are assumed equal, what is the total cost for each machine for 10k holes, assuming the total cost of each machine to be charged to these holes? (b) for how many holes will the costs be equal?Company XYZ is a farming company. The company are famous for producing strawberries and blueberries. The variable cost of producing and selling one box of strawberries is $3, while the variable cost of producing and selling one box blueberries is $5. Each box of strawberries is selling for $10, while a box of blueberries sells for $13. The company produces and sells 5 boxes of strawberries for every 2 boxes of blueberries. Assuming a fixed cost of ?$204,000. How many boxes of blueberries need to be produced and sold to achieve breakeven 20,000 a O 8,000 b O 1,600 .c O None of the given answers d O 4,000 .e OPatz 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
- Kofi Abebrese runs a small industrial company that specialize in the production of high standard windows for housing estates. A worker is paid GH¢0.9 per hour and can produce two window with an hour. Each window uses a frame costing GH¢1 and incur a variable overheads of GH¢0.7. Each window sells for GH¢3. Currently, due to the economic condition, work is rather slack and three employees are occupied in carrying out extensive repairs to Kofi Abebrese's own house. Kofi owns a warehouse next to the factory, which had been used as a factory store, in the past. It is now let out on a renewable annual lease of GH¢600. A new building company, Allied Consult, which specializes in the production of prefabricated houses has asked Kofi if he would be interested in accepting a contract for GH¢30,000 which will be for a year initially, to produced molded internal building sections. Kofi estimates that, the contract will take 13,200 hours of works, or the work of five men for a year, and that…LINEAR PROGRAMMING. A certain Repair Shop with only the owner doing the repair job would like to earn P3,000.00 for two days. On the average, he charges P500 per piece for the repair of one unit of laptop and P200 for the repair of each unit of one cellphone. He works for 8 hours a day. He spends on the average 2 hours to repair a unit of laptop and 1.5 hours to repair a cellphone. Using linear programming, determine how many units of laptops and how units of cellphone he must repair for two days in order for him to earn exactly P3,000.00 for two days. You may use linear equations and/or inequalities to arrive at the answers. Check the consistency of your answers.Kofi Abebrese runs a small industrial company that specialize in the production of high standard windows for housing estates. A worker is paid GHC0.9 per hour and can produce two window with an hour. Each window uses a frame costing GHC1 and incur a variable overheads of GHC0.7. Each window sells for GH¢3. Currently, due to the economic condition, work is rather slack and three employees are occupied in carrying out extensive repairs to Kofi Abebrese's own house. Kofi owns a warehouse next to the factory, which had been used as a factory store, in the past. It is now let out on a renewable annual lease of GHC600. A new building company, Allied Consult, which specializes in the production of prefabricated houses has asked Kofi if he would be interested in accepting a contract for GHC30,000 which will be for a year initially, to produced molded internal building sections. Kofi estimates that, the contract will take 13,200 hours of works, or the work of five men for a year, and that…
- A company has one machine which can be used to make product Alpha and product Beta. Each unit of product Alpha requires 45 minutes of machine time, while each unit of product Beta requires 37 minutes of machine time. The machine can be used for 8 hours per day and 5 days per week. Next week the company will produce 23 units of product Alpha. After completing the production of Alpha, the company will produce product Beta. How many units of product Beta can be produced next week? Use at least 4 decimals.You must showm your calculation steps and brief explanation on your Excel spreadsheets.Mark has a company that produces tables and chairs, both having two different models. The product models and related information are given in the following table. Wood costs 3000 $ per cubic meter and 200 m3 of wood are available for the upcoming month. The cost of labor is 40 $/hour and there are 6000 hours of labor available in a month. Mark sells his products to a big chain retail company. The company purchases all products whatever Mark produces. Mark formulates an LP as follows to determine the optimal monthly production plan such that he maximizes the total profit. Decision Variables: X1 : number of basic tables to be produced. X2 : number of elegant tables to be produced. X3 : number of basic chairs to be produced. X4 :number of elegant chairs to be produced. Max Z = 140 X1 + 345 X2 + 120 X3 + 260 X4 ( maximize total profit) Subject to 0.11 X1 + 0.13 X2 + 0.06 X3 + 0.07 X4 ≤ 200 (constraint on the available amount of wood) 2 X1 + 4.5 X2 + 1.5 X3 + 4 X4 ≤ 6000…4) A printing company makes three grades of wall posters. The better-quality posters sell for Rs. 2.50, intermediate quality for Rs.2.00 and the poorer quality poster for Rs. 1.50. Paper costs Rs. 0.75 for each of the better-quality posters and Rs.0.50 and Rs. 0.25 for each intermediate and poorer quality poster respectively. Because of poor quality paper, the less expensive posters require two minutes of printing time while the other two require 1 minute of printing time only. The department is allocated Rs.150 per day for paper. There are 480 minutes of printing time available daily and each minute that is used to estimate to cost the company Rs. 0.25. In addition, the department incurs a fixed daily cost of Rs. 125, which are not affected by the quantity and quality of papers produced. You are asked to suggest as to how much each type of posters is to produce in order to maximize daily profit?(Don't use excel shortcut solve manually by Simplex LPP method)
- A group of students organizes a bake sale in which they sell hundreds of cookies at$1 per piece. They set up a table on campus and wait for students to come and purchasetheir cookies. Consider the following variables in this bake sale operation:1. Size of the cookies2. Weather conditions on campus3. Organization of the table4. Number of cookies sold5. Competition from other fund-raisers coinciding on campus6. Amount of advertising and shouting of the students at the bake sale table7. Number of students on campus that dayWhich of these variables are input variables?a. 1 and 2b. 1 and 3c. 1, 3, and 5d. 1, 3, and 6A small scale industry manufactures electrical regulators, with a small group of semi-skilled workers both male and female. Due to limitations in space and finance, the number of workers employed cannot exceed 11 and their total salary cannot be more than Rs60, 000 per month. The male workers are paid Rs.6000 per month while the female workers are paid Rs. 5000 per month. It has been found that the male workers are swifter and since they are willing to work overtime, they contribute Rs.10, 000 per month as compared to Rs.8500 from their female counterparts. Apart from their salary, food coupons are provided: 6 coupons to per male employee and 5 coupons to per female employee. However, the total maximum amount of coupons that can be distributed are only 90. a) Formulate the model and find out how many male and female members should the company employ so as to maximize their contribution? b) If they make the female compensation equal to their male counterpart, should there be…A company manufactures both mountain bikes and trail bikes. The cost of materials for a mountain bike is $60, and the cost of materials for a trail bike is $40. The cost of labor to manufacture a mountain bike is $80, and the cost of labor to manufacture a trail bike is $60. During a week in which the company has budgeted $1,800 for materials and $2,500 for labor, how many mountain bikes does the company plan to manufacture? mountain bikes