From the information, observe that during the next four quarters, Dorian Auto must meet the demand for cars.

Consider the following events:

x_t = Number of cars produced at the beginning of each quarter(t=1,2,3,4)

d_t = Demand during each quarter t

i_t = Number of cars on hand at end of time t

Total cost (TC) = {cost of increasing quarterly production capacity+cost of maintaining a car of production capacity+variable cost of producing a car+holding cost}

Total cost (TC) = 100(x_t+1)+50(i_t+x_t-d_t)+2000x_t+150(i_t+x_t-d_t)

Inventory at end of quarter t={inventory at end of quarter(t-1)+(quartertproduction-demand oftquarter)}

i_t = i_t-1+(x_t-d_t)

For 1^st quarter,

i₁=300+x₁-4000

For 2^nd quarter,

i₂=i₁+x₂-2000

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Chapter 4, Problem 23RP

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Solution Summary: The author explains that Dorian Auto must meet the demand for cars during the next four quarters.

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