Cogent Technology Retail Store (profit/tablet) Supply Vendor Location Store 1 Store 2 Store 3 Store 4 Store 5 Store 6 Alum Rock $ 9 $ 8 $11 $12 $7 $ 8 26 Berkeley 10 10 8 6 7 40 Concord 6 6 7 4 20 Daly City 4 6 8 10 40 East Foothills 12 10 8 6 7 45 Demand 25 15 30 18 27 35

Here, t1,t2,t3,t4,t5,t6 be tablets supplied by Alum Rock vendor to store 1,2,3,4,5,6. t7,t8,t9,t10,t11,t12 be tablets supplied by Berkeley vendor to store 1,2,3,4,5,6. t13,t14,t15,t16,t17,t18 be tablets supplied by Concord vendor to store 1,2,3,4,5,6. t19,t20,t21,t22,t23,t24 be tablets supplied by Daly City vendor to store 1,2,3,4,5,6. t25,t26,t27,t28,t29,t30 be tablets supplied by East foothills vendor to store 1,2,3,4,5,6. Objective Function (It is sum product of tablets at individual stores & profit), Max Profit = 9*t1 + 8*t2+11*t3+12*t4+7*t5+8*t6+10*t7+10*t8+8*t9+6*t10+ 9*t11+7*t12 + 8*t13+6*t14+6*t15+5*t16 + 7*t17+4*t18 + 4*t19+6*t20+9*t21+5*t22+8*t23+10*t24+12*t25+10*t26+ 8*t27 + 9*t28 + 6*t29 + 7*t30 s.t., Supply constraint as follows, t1+ t2 +t3 +t4+t5 +t6 <= 26 t7 +t8 +t9 +t10 +t11 +t12 <=40 t13 +t14 +t15 +t16 +t17 +t18 <=20 t19 + t20+t21+t22+t23+t24 <=40 t25 + t26 +t27 +t28 +t29 +t30<=45 Demand Constraint as follows, t1+t7+t13+t19+t25>=25 t2+t8+t14+t20+t26 >=15 t3+t9+t15+t21+t27 >=30 t4+t10+t16+t22+t28 >= 18 t5+t11+t17+t23+t29>=28 t6+t12+t18+t24+t30>=35 where from t1 to t30, all values greater than or equal to zero Answer 1, Please find the attached working below in excel file-Answer 2, When a company purchase all table from a local vendor, Let assume, x1, x2, x3, x4, x5, x6 = Supply of tablet by local vendors to store 1, 2, 3, 4, 5, 6 respectively Objective Function is below- Max Profit = 9*x1+ 8*x2+ 9*x3 + 9*x4 +7*x5 +8*x6 s.t, x1>= 25 ; x2>=15 ; x3>=30 ; x4>= 18; x5>=27; x6>=35Even after the company buy full order from a local vendor, the profit that the company gets from a local vendor is less compare to the existing vendor. Therefore, the company must not buy with a local vendor for purchase of tablesAnswer 3, From the above calculation, when the company purchases tables from the listed vendor as per question 1.1, the profit is $1738. On the other hand when the company purchases all tables from a local vendor as per question 1.2, profit is $1435 which is low. Now if the unit table store profits from local vendors compare to other vendors, then per unit table profit are not highest. Therefore, the strategy for the company should be trying to purchase from its vendor base.

Answered: Cogent Technology Retail Store (profit/tablet) Supply Vendor Location Store 1 Store 2 Store 3 Store 4 Store 5 Store 6 Alum Rock $ 9 $ 8 $11 $12 $7 $ 8 26…

Practical Management Science

6th Edition

ISBN: 9781337406659

Author: WINSTON, Wayne L.

Publisher: Cengage,

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Question

Cogent Technology has computer stores on the West Coast. Their stores are set up like warehouse clubs focusing on high volume. Cogent Technology has a hub set up for their distribution. For instance, to serve the Silicon Valley area, a Cogent Technology warehouse is set up in San Jose to serve nearby stores. Cogent Technology warehouse managers generally purchase their items in bulk to get volume discounts from their vendors. Cogent Technology warehouse has an agreement with the vendors that they can return unsold inventory if it does not sell in six months. Cogent Technology has a policy of fulfilling all customer orders. In some cases when the store managers foresee a stockout situation, they are authorized to buy from other vendors rather than wait for the warehouse to deliver their items. In some cases, the prices bought directly by the store managers are cheaper than what the warehouses buy in bulk.

A good example of a sellable item is tablets. Cogent Technology warehouses purchase their stock from vendors based in Alum Rock, Berkeley, Concord, Daly City, and East Foothills and then ships it to its six stores in Silicon Valley. The vendors know that Cogent Technology retail stores are authorized to buy directly from other vendors so they decide to limit the number of tablets the warehouse can purchase. The table below shows the profit that Cogent Technology makes per tablet, based on which location the item is purchased and at which warehouse it is sold. The table also includes the available tablets per week at the retail locations and the display space available at each retail store per week.

1) Determine the most optimal model for Cogent Technology to maximize their profits. You may use a computer application to solve this problem.

2) If a Cogent Technology warehouse can buy all its tablets from a local store that will result in a profit of $7 per tablet at store 5; $8 per tablet at stores 2 and 6; and $9 per tablet at stores 1, 3, and 4, should Cogent Technology purchase all, some or none of its tablets from this vendor? Explain your answer quantitatively and qualitatively.

3) Recommend a strategy for Cogent Technology.