A car manufacturer produces 4 types of cars: compact, SUV, sedan, and custom, with sale prices set to $13,000, $28,000, $23,000 and $40,000 respectively. The manufacturingprocess involves two major steps: assembly and painting. The required numbers of hours pertype of car are as follows:

Compact SUV Sedan Custom
Assembly 4 9 7 10
Painting 1 1 3 40

The unumfacturer needs a production plait for one year in which there are 5,000 hours available for assembly and 4,250 man-hours for painting.
(a) Using xe = units of type i cars to produce, i = compact, SUV, sedan, and custom, formulate an LP (assuming this company can produce fractional number of cars) to determine an optimal manufacturing plan to maximize total revenue.
(b) write the dual of the LP in part a.