A computer manufacturer sells motherboards, CPUs, and cases. They only sell products in packages. Package 1 contains 1 motherboard(s) and 2 case(s). Package 2 contains 2 motherboard (s) and 3 CPU(s). Package 3 contains 3 case(s). In total, the company owns 30 motherboards, 27 CPUs, and 57 cases. What unique combination of package sales will allow the company to get rid of its entire inventory? Hint: You should set up and solve a linear system to find the answer. If you find it helpful, you are welcome to use numpy to solve the system. Package 1: Package 2: integer integer Package 3: integer ? ? ?

A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 1 unit of protein, 2 units of carbohydrates, and 1 unit of fat. Each ounce of nuts will supply 1 unit of protein, 1 unit of carbohydrates, and 1 unit of fat. Every package must provide at least 8 units of protein, at least 12 units of carbohydrates, and no more than 11 units of fat. Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package. a. Write a system of inequalities to express the conditions of the problem. b. Graph the feasible region of the system. a. Fill in the chart. Protein Carbohydrates Fat Fruit unit(s) per ounce unit(s) per ounce unit(s) per ounce Nuts unit(s) per ounce unit(s) per ounce unit(s) per ounce .. Requirements per package At least At least No more than unit(s) unit(s) unit(s)

A company that sells webcams has relocated production to 3 foreign plants: China.Turkey and Romania. After the first 20 days of production 2,380 webcams, or 28% of the total.came from Turkey and 46% from China. Quality control. carried out on all webcams discarded 119 Turkish webcams, 313 Chinese webcams and 199 Romanian webcams as defective. A webcam produced in China has a production cost of 3 euros, while one produced in Turkey has it of 5 euros Calculate: 1. the probability that a randomly chosen webcam is defective; 2. the probability that a webcam was produced in Romania, knowing that defective; 3. the probability that a webcam was manufactured in China, knowing that for sale (not defective);

An automobile company produces cars in Los Angeles and Detroit and has a warehouse in Atlanta.The company supplies cars to customers in Houston and Tampa. The costs of shipping a car betweenvarious points are listed in the table below, where a blank means that a shipment is not allowed. LosAngeles can produce up to 1100 cars, and Detroit can produce up to 2900 cars. Houston must receive2400 cars, and Tampa must receive 1500 cars. (Include your formulations to receive credit. Thinkcarefully about the transhipment locations.) (a) Determine how to minimize the cost of meeting demands in Houston and Tampa. (b) Modify the answer to part (a) if shipments between Los Angeles and Detroit are not allowed.  (c) Modify the answer to part (a) if shipments between Houston and Tampa are allowed at a cost of$5 per car.