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GENERAL LINEAR PROGRAMMING NOTATION 75

each, and labelling and filling costs are estimated to be E0.03 for each jar of salsa
produced. Miguel’s contract with Western Foods results in sales revenue of E1.64 for
each jar of Western Foods Salsa and E1.93 for each jar of Mexico City Salsa.
a. Develop a linear programming model that will enable Miguel’s to determine the mix of
salsa products that will maximize the total profit contribution.
b. Find the optimal solution.
16 As part of a quality improvement initiative, government employees complete a three-day
training programme on teamwork and a two-day training programme on problem solving.
The manager of quality improvement requested that at least eight training programmes on
teamwork and at least ten training programmes on problem solving be offered during the
next six months. In addition, senior-level management specified that at least 25 training
programmes must be offered during this period. A consultant is used to teach the training
programmes. During the next six months, the consultant has 84 days of training time
available. Each training programme on teamwork costs E10 000 and each training
programme on problem solving costs E8000.
a. Formulate a linear programming model that can be used to determine the number of
training programmes on teaming and the number of training programmes on problem
solving that should be offered in order to minimize total cost.
b. Graph the feasible region.
c. Determine the coordinates of each extreme point.
d. Solve for the minimum-cost solution.

17 Does the following linear programme involve infeasibility, unbounded and/or alternative
optimal solutions? Explain.
Max 4x 1 þ 8x 2
s:t:
2x 1 þ 2x 2 10
1x 1 þ 1x 2 8
x 1 ; x 2 0

18 Does the following linear programme involve infeasibility, unbounded and/or alternative
optimal solution? Explain.
Max 1x 1 þ 1x 2
s:t:
8x 1 þ 6x 2 24
4x 1 þ 6x 2 12
2x 2 4
x 1 ; x 2 0

19 Management of High Tech Services (HTS) would like to develop a model that will help
allocate their technicians’ time between service calls to regular contract customers and
new customers. A maximum of 80 hours of technician time is available over the two-
week planning period. To satisfy cash flow requirements, at least E800 in revenue (per
technician) must be generated during the two-week period. Technician time for regular
customers generates E25 per hour. However, technician time for new customers only
generates an average of E8 per hour because in many cases a new customer contact
does not provide billable services. To ensure that new customer contacts are being
maintained, the technician time spent on new customer contacts must be at least
60 per cent of the time spent on regular customer contacts. Given these revenue and
policy requirements, HTS would like to determine how to allocate technician time

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