Chapter 8.4, Problem 86AE

Computing Profit Rizza Ford has two locations, one in the city and the other in the suburbs. In January, the city location sold 400 subcompacts, 250 intermediate-size cars, and 50 SUVs; in February, it sold 350 subcompacts, 100 intermediates, and 30 SUVs. At the suburban location in January, 450 subcompacts, 200 intermediates, and 140 SUVs were sold. In February, the suburban location sold 350 subcompacts, 300 intermediates, and 100 SUVs.

a. Find 2 by 3 matrices that summarize the sales data for each location for January and February (one matrix for each month).

b. Use matrix addition to obtain total sales for the 2-month period.

c. The profit on each kind of car is $\$100$ per subcompact, $\$150$ per intermediate, and $\$200$ per SUV. Find a 3 by matrix representing this profit.

d. Multiply the matrices found in parts (b) and (c) to get a by 1 matrix showing the profit at each location.