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}

During the year, the delph company had no beginning or ending inventories and it started, completed, and sold only two jobs—job d-75 and job c-100. it provided the following information related to those two jobs: job d-75: molding fabrication total direct materials cost $ 375,000 $ 325,000 $ 700,000 direct labor cost $ 200,000 $ 160,000 $ 360,000 machine-hours 15,000 5,000 20,000 job c-100: molding fabrication total direct materials cost $ 300,000 $ 250,000 $ 550,000 direct labor cost $ 175,000 $ 225,000 $ 400,000 machine-hours 5,000 25,000 30,000delph had no overapplied or underapplied manufacturing overhead during the year. assume delph uses a plantwide overhead rate based on machine-hours.1-a. compute the predetermined plantwide overhead rate.1-b. compute the total manufacturing costs assigned to job d-70 and job c-200.1-c. if delph establishes bid prices that are 150% of total manufacturing costs, what bid price would it have established for job d-70 and job c-200? 1-d. what is delph's cost of goods sold for the year? assume delph uses departmental overhead rates based on machine-hours.2-a. compute the predetermined departmental overhead rates.2-b. compute the total manufacturing costs assigned to job d-70 and job c-200.2-c. if delph establishes bid prices that are 150% of total manufacturing costs, what bid price would it have established for job d-70 and job c-200? 2-d. what is delph's cost of goods sold for the year?