Explanation of Solution
Given:
Let
Let
Objective function:
Considering the constraints,
Constraint 1: Drug 1 must contain at least 65% of chemical 1.
Constraint 1: Drug 2 must contain at least 55% of chemical 1
Constraint 3: At most 100 oz of raw material available.
Constraint 4: At most 120 hours of skilled labor available.
Constraint 5: Chemical 1 used should be less than amount of chemical 1 produced.
Constraint 5: Chemical 2 used should be less than amount of chemical 2 produced.
Expressing the constraint 1 in terms of variables:
Expressing the constraint 2 in terms of variables:
Expressing the constraint 3 in terms of variables:
Expressing the constraint 4 in terms of variables:
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Introduction to mathematical programming
- Question 34 Frontline Agricultural Processing Systems uses several ingredients to make wheat crackers. After several years of operations and testing, their scientists found high protein and carbohydrates in two of their ingredients, barley and corn. While an ounce of barley costs $0.25, an ounce of corn costs $0.46. While an ounce of barley provides 9 mg of protein and 1 mg of carbohydrates, an ounce of corn provides 7 mg of protein and 5 mg of carbohydrates. Recently, demand for wheat crackers has increased. To lower the overall cost of producing wheat crackers, Frontline Agricultural Processing Systems will want to know how many ounces of barley and corn to include in each box of wheat crackers to meet the minimum requirements of 160 milligrams of protein and 40 milligrams of carbohydrates. If the carbohydrate requirement is reduced by 2 milligrams, how much reduction would the optimal cost change by? Round to 2 decimal places.arrow_forwardIn the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two different lots. This occurs when holding tanks are replenished and the remaining portion of a lot is insufficient to fill the tanks. Only 5% of batches with material from a single lot require reprocessing. However, the viscosity of batches consisting of two or more lots of material is more difficult to control, and 40% of such batches require additional processing to achieve the required viscosity. Let A denote the event that a batch is formed from two different lots, and let B denote the event that a lot requires additional processing. Determine the following probabilities:a. P(A) b. P(A’) c. P(B|A) d. P(B|A’) e. P(A∩B) f. P(A∩B’) g. P(B)arrow_forwardA company manufactures two types of trucks. Each truck must go through the painting shop and the assembly shop. If the painting shop were completely devoted to painting type 1 trucks, 800 per day could be painted, whereas if the painting shop were completely devoted to painting type 2 trucks, 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, 1500 per day could be assembled, whereas if the assembly shop were completely devoted to assembling truck 2 engines, 1200 per day could be assembled. It is possible, however, to paint both types of trucks in the painting shop. Similarly, it is possible to assemble both types in the assembly shop. Each type 1 truck contributes $1000 to profit; each type 2 truck contributes $1500. Use Solver to maximize the company’s profitarrow_forward
- • A certain grade of steel is graded according to the following conditions: (i) Hardness must be greater than 100 (ii) Carbon content must be less than 0.8 (iii) Tensile strength must be greater than 5500 The grades are as follows: Grade is 10 if all three conditions are met Grade is 9 if conditions (i) and (ii) are met Grade is 8 if conditions (ii) and (iii) are met Grade is 7 if conditions (i) and (iii) are met Grade is 6 if only one condition is met Grade is 5 if none of the conditions are met Write a program, which will require the user to give values of hardness, carbon content, and tensile strength of the steel under consideration, and output the grade of the steel. Comment/Discussion on the obtained results and discrepancies (if any).arrow_forwardMaps Remaining Time: 58 minutes, 28 seconds. Question Completion Status: QUESTION 11 Rs 120 2 Vs 20 V RL The source in Figure 2 has an internal resistance of 120 Ohm. Determine the load power for each of the following values of the variable load resistance (a) 00 O a. 330 mW O b.0 mW O c. 450 mW O d. 500 mWarrow_forwardPROBLEM 9 The Darby Company manufactures and distributes meters used to measure electric power consumption. The company started with a small production plant in El Paso and gradually built a customer base throughout Texas. A distribution center was established in Fort Worth, Texas, and later, as business expanded, a second distribution center was established in Santa Fe, New Mexico. The El Paso plant was expanded when the company began marketing its meters in Arizona, California, Nevada, and Utah. With the growth of the West Coast business, the Darby Company opened a third distribution center in Las Vegas and just two years ago opened a second production plant in San Bernardino, California. Manufacturing costs differ between the company's production plants. The cost of each meter produced at the El Paso plant is $10.50. The San Bernardino plant utilizes newer and more efficient equipment; as a result, manufacturing costs are $0.50 per meter less than at the El Paso plant. Due to the…arrow_forward
- Pneumatics Engineering purchased a machine that had a fi rst cost of $40,000, an expected useful life of 8 years, a recovery period of 10 years, and a salvage value of $10,000. The operating cost of the machine is expected to be $15,000 per year. The inflation rate is 6% per year and the company’s MARR is 11% per year. Determine the depreciation charge for year 3 according to the straight line method. (UNITS ARE REQUIRED)arrow_forwardA factory produces two types of wood blocks with 2m and 4m lengths. The blocks are moved by a conveyor belt and passing under two photocells A and B spaced by 3m apart as shown in the following figure. The blocks are separated by more than 4m. A trap door is placed immediately to the right of photocell B. To separate the two types of blocks, it is required that the trap door should open when the small block pass under Band close when the blocks passed beyond B. The door opens when the output (2) of state machine is logic 1. The designer needs for . AND-gate(s) for implementing the aforementioned state machine (2) a d> 4m 3m 0.25marrow_forwardA factory produces two types of 2 points wood blocks with 2m and 4m lengths. The blocks are moved by a conveyor belt and passing under two photocells A and B spaced by 3m apart as shown in the following figure. The blocks are separated by more than 4m. A trap door is placed immediately to the right of photocell B. To separate the two types of blocks, it is required that the trap door should open when the small block pass under B and close when the blocks passed beyond B. The door opens when the output (Z) of state machine is logic 1. How many states the designer needs for drawing the minimal Mealy state diagram? * d> 4m 3m 0.25m 6. 5 4.arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole