Solution:$70,000 Sale price x 5.5% Commission rate = $3,850 Total commission$3,850 Total commission x 20% Listing sales associate = $770 Listing sales associate share$3,850 Total commission - $770 Listing sales associate share = $3,080$3,080 Split with broker /2 = $1,540 sales associate's commission
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The highway department has decided to add exactly 300 km of highway and exactly 200 km of expressway to its road system this year. The standard price for road construction is $2 million per kilometer of highway and$8 million per kilometer of expressway. Only two contractors, company A and company B, can do this kind of construction, so the entire 500 km of road must be built by these two companies. However, company A can construct at most 400 km of roadway (highway and expressway), and company B can construct at most 300 km. For political reasons, each company must be awarded a contract with a standard price of at least $300 million (before discounts). Company A offers a discount of$2000 per kilometer of highway and $6000 per kilometer of expressway; company B offers a discount of$3000 for each kilometer of highway and $5000 for each kilometer of expressway.
(a) Let x and y represent the number of kilometers of highway and expressway, respectively, awarded to company A. Show that the total discount received from both companies is given bywhere D is in thousands of dollars.
(b) The highway department wishes to maximize the total discount D. Show that this problem is equivalent to the following (b) The highway department wishes to maximize the total discount D. Show that this problem is equivalent to the following linear programming problem, by showing exactly how the first six constraints arise: Maximizesubject to$
(c) Find the values of x and y that maximize D.