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The matrix below shows the selling price (in USD) of three snack packs S1,S2 and S3 at two vending machines A and B.
A student club places an order of 50 of S1, 80 of S2, and 40 of S3.
Write down a matrix equation for the total revenue vector R (2×1) from each machine.
Hence calculate the total revenue from vending‑machine A and from vending‑machine B.
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The regional sales of three products A, B and C by two branches, North and South, are given (in units) by the matrix
where the first row is North and the second is South. The shipping rate (in $USD per unit) charged by Carrier 1 and Carrier 2 for each product is
where rows correspond to products A, B, and C and columns to Carriers 1 and 2 respectively.
Write down a matrix equation for the total shipping‑cost matrix C, and hence find C.
For each branch, state which carrier is cheapest.
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The number of tilapia, catfish and trout harvested (in units) by Farm A and Farm B during a season is given by the matrix
where the first row is Farm A and the second is Farm B. Each fish species has an average weight (kg) and a selling price (USD) per fish, as shown by
where rows correspond to tilapia, catfish and trout, and columns correspond to weight and price respectively.
Find the total weight–revenue matrix T.
For each farm, determine
the total weight harvested (kg);
the total revenue earned (USD);
Hence state which farm has the higher revenue per kg.
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A system of equations is given by
Write this system in the form Ax=b, and find A−1.
Hence solve for (x,y,z).
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