Question

A manufacturing company receives orders for engines from two assembly plants. Plant I needs at least 45 ​engines, and plant II needs at least 32 engines. The company can send at most 140 engines to these assembly plants. It costs $30 per engine to ship to plant I and ​$40 per engine to ship to plant II. Plant I gives the manufacturing company ​$20 in rebates toward its products for each engine they​buy, while plant II gives similar ​$15 rebates. The manufacturer estimates that they need at least ​$1500 in rebates to cover products they plan to buy from the two plants. How many engines should be shipped to each plant to minimize shipping​costs? What is the minimum​ cost?

a.) How many engines should be shipped to each plant to minimize shipping​ costs, subject to the given​ constraints?

The number of engines to send to plant I is ____.

The number of engines to send to plant II is ____.

b.) What is the minimum shipping cost, subject to the given constraints?

Answer 1

let number of engunes ehupped to plant plant Cost to shup engute to plant plant 30 one 40 2 then total Cost 40y We need to shup atbast 45 and 8aengunes to plant 302t 5engnes tolat C7 45 Total, rebates provided by the plants has to be arealen than or auals 1500 Total number o engunes shupped has to be equal 140 lees than or 140 obyechwe Aundion minimize So ou1 s140 Subject to OC 45 Y>32 > 1500 aoxt 15

20x15y1500 100 the shaded region is the feasible region (45, 95) -50 (45, 40) (108, 32) y= 32 (51, 32) x+y= 140 -50 50 100 150 x = 45

Comenpounla: (45,45), (45,40), (5, 32) C108,32) - 40 Nentex C Box+ C4S,) 5150 SI50 (51,32) 3000 5280 The mwimum Cost 3000 when x51 The number & engines send to plant The number engunés iS 51 send to planta is 32

Answer 2

what is the minimum shipping cost, subject to the given constraints?