A steam plant burns two types of coal: anthracite (A) and bituminous (B). For each ton of A burned, the plant produces 27.6 millon Btu of heat, 3100 grams (g) of sulfur dioxide, and 250 g of particulate matter (solid-particle pollutants). For each ton of B burned, the plan produces 30.2 million Btu, 6400 g of sulfur dixoide, and 360 g of particulate matter.

a. How much heat does the steam plant produce when it burns x1 tons of A and x2 tons of B?

b. Suppose the output of the steam plant is described by a vector that lists the amounts of heat, sulfur dioxide, and particulate matter. Express this output as a linear combination of two vectors, assuming that the plan burns x1 tons of A and x2 tons of B.

c. [M] Over a certain time period, the steam plant produced 162 million Btu of heat, 23,610 g of sulfur dioxide, and 1623 g of particulate matter. Determine how many tons of each type of coal the steam plant must have burned. Include a vector equation as part of your solution.

{Note to Tutor: I've attached my work but I am having trouble putting the augmented matrix in part c in reduced echelon form}

At which level will a manager use analytics to make decisions? operational level managerial level strategic level all of the above

In return for their with optimizing his painting project, the castle servant informed poly and digit that he saw someone dressed as the king leaving behind a trail of crumbs as he walked into the jester's room late last night. poly and digit have finally found the crisp-collecting culprit — it turns out the jester's shoe size and hair color match the clues that were found! in gratitude, poly and digit agree to the servant with his current task of replacing all of the tables and chairs in the castle. his goal is to determine which furniture company should produce the new furniture. he receives information from a company that customizes elegant furniture, and he wants to analyze the company's production process in order to calculate some problems about cost and availability. read the following scenario, and assist poly and digit as they the servant with his calculations. the fit for a king furniture company requires 2020 hours of labor to produce a standard table, and a chair requires 1212 hours of labor. the labor available is 565565 hours per week. the company can produce at most 3535 chairs per week.

Skychefs, inc. prepares in-flight meals for a number of major airlines. one of the company's products is grilled salmon in dill sauce with baby new potatoes and spring vegetables. during the most recent week, the company prepared 4000 of these meals using 960 direct labor hours. the company paid these direct labor workers a total of $19,200 for this work, or $20.00 per hour. according to standard cost card for this meal, it should require 0.25 direct labour-hours at a cost of $19.75 per hour.1. what is the standard labor-hours allowed (sh) to prepare 4,000 meals? 2. what is the standard labor cost allowed (sh x sr) to prepare 4,000 meals? 3. what is the labor spending variance? 4. what is the labor rate variance and the labor efficiency variance?