Question

A company produces three different type of chocolates. A, B, and C. The sales volume for A is at least 50 % of the total sales of all three chocolates. However, the company cannot sell more than 75 units of A per day. The three types of chocolate use one raw material, of which the maximum daily availability is 240 lb. The usage rates of the raw material are 2 lb per unit of A, 4 lb per unit of B, and 3 lb per unit of C. The unit prices for A, B, and C, are $20 $50 and $35, respectively.

a. Develop a mathematical model that determine the optimal product mix for the company.

b. Solve it using software and show the results.

c. If available raw material is increased by 120 lb, determine the change in total revenue using the result in question b above.

d. Determine the effect of increasing or decreasing the maximum demand for product A by 10 units.

Answer 1

a)

Mathematical model is as follows:

Let A, B, C be the number of units of chocolate A, B, C to be produced per day

Max 20A+50B+35C

s.t.

A >= 0.5*(A+B+C)

or,

0.5A-0.5B-0.5C >= 0

A <= 75

2A+4B+3C <= 240

A, B, C >= 0

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b)

Solution using LINGO software is as follows:

Optimal solution:

A = 40

B = 40

C = 0

Objective value = 2800

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c)

Solution Report - Lingo 1

Dual price of raw material constraint (row 4) is 11.67

If available raw material is increased by 120 lb, change in total revenue = Dual price * change in raw material

= 120*11.67

= 1400 (this is the increase in revenue, in addition to 2800)

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d)

Solution Report - Lingo 1

Dual price of maximum demand of product A (row 3) is 0

Also, optimal quantity of A is 40 , which is 35 less than maximum demand of 75.

If maximum demand for product A is increased or decreased by 10 units, change in total revenue = 0