5-13 Marc Smith's construction firm currently has three projects under way in various counties in Iowa. Each requires a specific supply of gravel. Three gravel pits are available in Iowa to provide for Smith's needs, but shipping costs differ from location to location. The following table summarizes the problem Smith faces: TONNAGE FROM JOB I JOB 2 JOB 3 ALLOWANCE Waterloo pit $9 $ 8 $ 7 1,500 Des Moines pit $7 $11 $ 6 1,750 Iowa City pit $4 $ 3 $12 2,750 Job requirements (tons) 2,000 3,000 1,000 (a) Determine Smith's optimal shipping quantities so as to minimize total transportation costs. (b) Examining the map, Smith recognizes that Jobs 1 and 2 are very near Iowa City. Rather than ship gravel directly from the Waterloo and Des Moines pits to these job sites, Smith wonders if it would be better for him to consolidate shipping at Iowa City. Given the excellent roads between major cities in Iowa, he believes he can ship gravel between Waterloo and Iowa City and between Des Moines and Iowa City for as little as $2 per ton. Set up and solve Smith's problem with this new information