4. The times (in minutes) required for assembling,
testing, and packaging large and small capacity food processors
are shown in the following table:
(a) Define a matrix T that summarizes the above data.
(b) Let M =[100 200] represent the number of large and small food processors
ordered , respectively. Find
MT and explain the meaning of its entries.
(c) If assembling costs $3 per minute, testing costs $1 per minute, and
packaging costs $2 per minute, find a
matrix C that, when multiplied with T, gives the total cost for making each size
of food processor.
5. If , find A-1.
6. If find B-1.
7. Solve the following system of equations using matrix
8. A small village has two major industries: steel and
electronics. For each unit of steel produced, 0.02 units of steel
and 0.15 units of electronices are used by the village. For each unit of
electronics produced, 0.1 units of steel and
0.01 units of electronics are used by the village. The remaining steel and
electronics products are then available to
export to a local city. If that city demands 500 units of steel and 800 units of
electronics, how many units of steel
and electronics pruducts should be produced by the village to meet its own needs
and those of the city?
9. Consider three sectors of the US economy: crude
petroleum (crude), petroleum-refining and related industries
(refining), and chemical production (chemical). The following table gives the
number of units of crude, refining,
and chemical products consumed in the production of one unit of crude product,
one unit of refining product, and
one unit of chemical product.
(a) What is the input-output matrix for this problem?
(b) Explain the meaning of the entries in row 1 of this matrix.
(c) How many units of refining products are consumed in the production of 7,500
units of crude product?
(d) How many units of chemical products are required to produce 500 units of
each sector in this economy?
(e) If a neighboring city demands 5,500 units of crude
products, 6,750 units of refining products, and 1,250 units
of chemical products, how much should this economy produce to satisfy internal
consumption and meet the
(f) Referring to (e), how many units of each product are consumed internally in
meeting the other city’s demands?
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